ELEMENTARY PRINCIPLES OF FLUID PRESSURE. 



(a 4-6-f- c) Xnu aXp 



and finally by division, we have 

 _aXpa-\-bXrb-\-cXvc 

 (a + b + c) 



Now, n u is the distance of the common centre of gravity of the 

 three bodies a, b and c, from A B c D the plane to which they are 

 referred ; hence again, the truth of the proposition is manifest, and 

 if another body were added to the system, a similar investigation 

 would exhibit the same law, and thus we might proceed to any extent 

 at pleasure, the nature of the induction being fully disclosed. 



COROL. If therefore, we suppose the system to be constituted of an 

 indefinite number of small bodies or particles of matter, it will become 

 assimilated to a fluid mass, and consequently, the proposition which 

 we have just demonstrated in reference to the centre o'f gravity, is 

 identified with the well-known theorem for estimating the pressure of 

 fluids ; to which subject we must now return. 



13. Resuming therefore, the conditions specified in Proposition I 

 preceding, let us suppose that ABCD, de- 

 notes a vertical section of a reservoir full of 

 water, E and F representing the corresponding 

 sections of the walls or embankments by 

 which it is contained ; then, since the fluid 

 is supposed to be quiescent or in a state of 

 equilibrium, it follows, that the surface AB is parallel to the horizon. 



Let b df hkm\>e the portion of the containing section or boundary, 

 on which the pressure exerted by the water is required to be investi- 

 gated, and conceive it to be constituted of an indefinite number of 

 minute bodies or particles of matter, placed at infinitely small dis- 

 tances from one another, or so near, that their aggregate or sum shall 

 make up the entire area which forms the subject of our investigation. 



Suppose the points b, d, f, A, k and m, to be so many individual 

 particles of the surface pressed, and through the points thus assumed 

 draw the vertical lines b a, dc,fe, hg, ki and m /, which lines are 

 severally in the direction of gravity, and consequently perpendicular 

 to the surface of the fluid, indicating by their lengths, the respective 

 depths of the several bodies of which our immediate system is corn- 



But according to Proposition I, the pressures exerted by the fluid 

 on the particles 6, d,f, h, k and m, are respectively represented by 

 the products 



b X ba, dXe?c,/X fe, h X h g, k X k i and m X m I, 



