CHAPTER VI. 



THE THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION 

 OF SOME HYDROSTATIC ENGINES. 



1. OF THE HYDROSTATIC OR BRAMAH PRESS. 



PROPOSITION II. 



121. IF there be any number of pistons of different magni- 

 tudes, any how applied to apertures in a cylindrical vessel filled 

 with an incompressible and non-elastic fluid : 



The forces acting on the piston to maintain an equilibrium, 

 will be to one another as the areas of the respective apertures, 

 or the squares of the diameters of the pistons. 



Let ABC D represent a section passing along the axis of a cylindrical 

 vessel filled with an incompressible and non-elastic 

 fluid, and let E,F be two pistons of different magni- 

 tudes, connected with the cylinder and closely fitted 

 to their respective apertures or orifices ; the piston 

 F being applied to the aperture in the side of the 

 vessel, and the piston E occupying an entire section 

 of the cylinder or vessel, by which the fluid is contained. 



Then, because by the nature of fluidity, the pressures on every part 

 of the pistons E and F, are mutually transmitted to each other through 

 the medium of the intervening fluid ; it follows, that these pressures 

 will be in a state of equilibrium when they are equal among them- 

 selves. 



Now, it is manifest, that the sum of the pressures propagated by 

 the piston E, is proportional to the area of a transverse section of the 

 cylinder ; and in like manner, the sum of the pressures propagated by 

 the piston F, is proportional to the area of the aperture which it 

 occupies; consequently, an equilibrium must obtain between these 

 pressures : 



