B 



EQUILIBRIUM OF PRESSURES. 



where we suppose the point B to be taken. Hence any 

 pressure, applied to the surface of an incompressible 

 fluid at rest, is transmitted equally to all parts of the 

 fluid and to its whole surface. 



COR. If a point E, be within a liquid, the pressure 

 transmitted from the piston A, to a plane surface of given 

 area, and having its centre at E, is constant for every pos- 

 sible position of the plane, and is always perpendicular 

 to it. 



9. The Pressures on Two Pistons are in Equi- 

 librium when Proportional to their Areas. Let 

 Fig. 4 represent a vessel with two apertures, in which pis- 

 tons are fitted ; and let the vessel be 

 filled with any liquid. Now, any 

 pressure applied to the small piston p, 

 will be transmitted by the liquid to 

 the large piston P, so that every por- 

 tion of surface in the large piston 

 will be pressed upwards with the same 

 force that an equal portion of surface 

 in the small piston is pressed down- 



Fig. 4 



wards (Art. 8). Let a = the area of the piston p, A = the 

 area of the piston P, p = the whole pressure applied to the 

 small piston p, and P = the whole pressure produced upon 

 the large piston P ; then, since the whole pressure on the 

 large piston is equal to that on the small one taken as many 

 times as the area of the small one is contained in that of 

 the large, we have for equilibrium, 



= px-' or .L-4. 

 ' p ~~ a 



(1) 



That is, tiro forces applied to pistons which are con- 

 nected with each other through the intervention of 

 some confined liquid, will be ' in equilibrium when 



