KQVlLlORtuM Of PRESSURES. 



they are directly proportional to the areas of the 

 pistons upon which they act. 



This result is wholly independent of the relative dimen- 

 sions and positions of the pistons. Let a be the unit of 

 area, say a square inch or square foot, then will p be the 

 pressure applied to the unit of area, and (1) becomes 



P=pA. (2) 



That is, the pressure transmitted to any portion of the 

 surface of the vessel is equal to that applied to the 

 unit of surface multiplied by the area of the surface 

 to ivhich the pressure is transmitted. 



If the area of the piston P be one square foot, and a 

 pressure of 10 Ibs. is applied at the piston p, it follows from 

 (2) that a pressure of 1440 Ibs. will be transmitted to the 

 piston P, and this must be counteracted by a pressure of 

 1440 Ibs. on that piston. Also, the interior of the vessel 

 will sustain an outward pressure of 10 Ibs. on every square 

 inch of its surface. And if the pressure on the piston p, is 

 increased till the vessel bursts, the fracture is as likely to 

 occur in some other part as in that towards which the force 

 is directed. 



COR. If in the vessel (Fig. 4) the piston A, be made 

 sufficiently large, the pressure transmitted from a to A may 

 be increased indefinitely ; a very great weight upon A may 

 be raised by a small pressure at a, the weight lifted being 

 greater in proportion to the size of A, or inversely to the 

 size of a. To increase the upward force at A, we must 

 enlarge the surface of A or diminish the surface of a, and 

 the only limitation to the increase of the force at A will be 

 the want of sufficient strength in the vessel to resist the 

 increased pressure. 



On this principle, machines of immense mechanical 

 power are constructed, which will be described in a future 

 chapter. 



