OF FLUID PRESSURE UPON THE INTERIOR OF CONICAL VESSELS. 109 



and because the weight of any quantity or mass of fluid, is propor- 

 tional to the magnitude and specific gravity jointly ; it follows, that if 

 w' denote the weight of the circumscribing column of fluid, we obtain 

 w/z=.7854/3 2 Ds. (81). 



COROL. Now this expression is precisely the same, as that which we 

 obtained for the pressure on the bottom, indicated by the equation 

 marked (72) ; hence it appears, that when the sides of the vessel 

 converge from the extremities of the diameter of its base towards each 

 other : 



The pressure on the base or bottom of the vessel, is equal to 

 the weight of a column of the fluid, of the same magnitude 

 as the cylinder circumscribing the conic frustum, or the vessel 

 by which the fluid is contained. 



But the circumscribing cylinder is manifestly greater than the conic 

 frustum ; consequently, the pressure upon the base or bottom of the 

 vessel, is greater than the weight of the fluid which it contains ; and 

 it is obvious, that the additional pressure arises from the re-action of 

 the converging sides. 



5. WHEN THE VESSEL REPRESENTS AN INVERTED TRUNCATED CONE, 

 WITH ITS AXIS PERPENDICULAR TO THE HORIZON. 



116. If the sides of the vessel diverge from the extremities of the 

 base, as represented in the subjoined diagram ; then, it may be 

 shown, that the weight of the fluid which the vessel contains, exceeds 

 the pressure upon its" base. 



Let ABCD be a vertical section, passing 

 along the axis of a vessel in the form of a 

 conic frustum, and which is filled with an 

 incompressible fluid whose horizontal surface 

 is AB ; the greater base of the frustum being 

 uppermost, or which is the same thing, the 

 sides diverging from the extremities of the lower diameter. 



Bisect the diameters A B and c D respectively in the points m and n ; 

 draw mn, and through the points D and c, the extremities of DC, draw 

 the straight lines Da and cb respectively parallel to mn, and meeting 

 AB in the points a and b; then is abcn a vertical section passing 

 along the axis of the inscribed cylinder. 



Draw the diagonal AC, dividing the trapezoid ABCD, into the two 

 triangles ABC and ADC; bisect the diagonal AC in the point t, and 



