ELEMENTARY PRINCIPLES OF FLUID PRESSURE. 



PROPOSITION I. 



10. When an incompressible and non-elastic fluid is in a state 

 of equilibrium, and subjected only to the action of gravity: 



The magnitude, or the intensity of pressure exerted by the 

 fluid, perpendicularly to any surface immersed in it, or other- 

 wise exposed to its influence, is measured by the weight of a 

 column of the fluid, whose base is eqval to the area pressed, 

 and whose altitude is the same as the depth of the centre of 

 gravity of that area beneath the upper surface of the fluid. 



This is an elegant and most important proposition in the doctrine of 

 fluid pressure, and in order that the principle may be the more readily 

 perceived, and the demonstration the more easily comprehended, it 

 will be proper, in the first place, to exhibit and demonstrate an analo- 

 gous property, in reference to the common centre of gravity of a 

 system of bodies, or of the particles of matter of which the system is 

 composed. 



The property which we have alluded to above, is noticed by almost 

 every writer on the principles of mechanical science, and it has at 

 various times received most beautiful and rigorous demonstrations ; it 

 may therefore, at first sight, appear superfluous to introduce it here; 

 but in order to bring the subject more immediately before the atten- 

 tion of our readers, we do not hesitate to repeat the process. 



PROPOSITION (A). 



11. If there be any system of bodies and a plane given in position 

 with respect to them : 



The distance of that plane from the common centre of 

 gravity of the system, is equal to the aggregate of the pro- 

 ducts, arising from multiplying each body into its distance 

 from the given plane, divided by the sum of the bodies. 



The proposition just enunciated, being of the greatest use in many 

 departments of philosophical inquiry, and of essential importance in 

 establishing the truth of the hydrodynamic principle above specified, 

 we shall therefore bestow some attention on its illustration for the 

 purpose of rendering it as clear as possible, by connecting the steps 

 with separate diagrams, -and pursuing the reasoning, until we shall 

 have proceeded so far that the law of induction becomes manifest, and 

 from thence, the truth of the principle announced in the proposition. 



To accomplish this purpose, let a and b, be two very small bodies 



E 2 V 



