OF FLUID PRESSURE UPON THE INTERIOR OF CONICAL VESSELS. 107 



Is situated in the axis, and at the same distance from its 

 extremities, as is the centre of gravity of the trapezoid, which 

 is a vertical section passing along the axis of the solid. 



Therefore, since by the construction, the point G has been shown to 

 be the centre of gravity of the trapezoid, it is also the centre of gravity 

 of the surface of the conic frustum, and TWO is its perpendicular depth 

 below the surface of the fluid. 



Put AZZ: the area of the base or bottom of the vessel, whose diameter 



is DC, 

 v=mn, the perpendicular depth of its centre of gravity, or the 



length of the axis of the vessel, 

 a the curve surface of the conic frustum, 

 d^nmo, the perpendicular depth of the centre of gravity, 

 /3 zz: DC, the diameter of the base or bottom of the vessel, 

 S zz: AB, the diameter of the top, 

 Pzz: the pressure on the bottom, 

 p HZ the pressure on the curve surface, 

 wzz: the weight, and s the specific gravity of the fluid. 



Then, according to the principles of mensuration, the area of the 

 lower base of the conic frustum, or the bottom of the vessel on which 

 the fluid presses, becomes 



A = . 7854/3% 

 and consequently, the pressure which it sustains, is 



Pzz:. 7854 /3 2 DS. (72). 



In the next place, the area of the curved surface of the conic 

 frustum, or the sides of the vessel containing the fluid, is 



a= 1.5708 08 + 3)X V** + 1 (ft W I 

 and therefore, the pressure which it sustains, is 



p = 1.5708 ()8 4- 5) ds VD* 4- 403 S) 2 . (73). 



Now, according to the writers on mechanics, the depth of the centre 

 of gravity of the trapezoid ABCD, below the horizontal line AB, is 

 obtained in the following manner : 



3 (/3 4 3) : D : : 2/3 4 3 : d, 

 and by equating the products of the extremes and means, we get 



therefore, dividing by 3 (/3 4- 3), we obtain 

 _ 

 = 



