8 ELEMENTARY PRINCIPLES OF FLUID PRESSURE. 



Now, it is obvious, that the expression 5 a s indicates the weight of 

 a column of the fluid, the area of whose base is a, perpendicular alti- 

 tude S, and the specific gravity s ; hence the truth of the proposition 

 is manifest. 



COROL. From what has been demonstrated above, it appears, that 

 whatever may be the form of the surface on which the fluid 

 presses, if its area, and the position of its centre of gravity can be 

 ascertained, the intensity of pressure which it sustains, is from thence 

 assignable. 



The truth of the proposition being thus established, we shall proceed 

 to deduce from it a few of the most useful and obvious inferences. 



14. INF. 1. If different planes be immersed perpendicularly, hori- 

 zontally, or obliquely, in fluids of different specific gravities : 



The pressures upon those planes perpendicularly to their 

 surfaces, are as their areas, the perpendicular depths of their 

 centres of gravity, and the specific gravities of the fluids 

 jointly. 



15. INF. 2. If different planes be immersed perpendicularly, hori- 

 zontally, or obliquely in the same fluid : 



The pressures upon those planes perpendicularly to their 

 surfaces, are as their areas, and the perpendicular depths of 

 their centres of gravity. 



16. INF. 3. If a plane surface of given dimensions be parallel to 

 the surface of the fluid in which it is immersed : 



The pressure sustained by the plane, in a direction perpen- 

 dicular to its surface, varies directly as its vertical depth 

 below the upper surface of the fluid. 



17. INF. 4. If a plane surface of given dimensions be any how 

 inclined to the surface of the fluid in which it is immersed : 



The pressure sustained by the plane, in a direction perpen- 

 dicular to its surface, varies directly as the vertical depth of 

 its centre of gravity, below the upper surface of the fluid. 



18. INF. 5. If any number of planes of equal areas be immersed 

 in the same fluid, and have their centres of gravity at the same vertical 

 depth below the surface : 



The pressures which they sustain are equal to one another, 

 whatever be their form, and whatever be their position with 

 respect to the surface of the fluid. 



19. INF. 6. If any plane surface revolve about its centre of gravity, 

 which remains fixed in position : 



