ON THE CONCAVE SURFACE OF A VESSEL. 177 



for water, it is 

 p' zz 28.2744X 8 X 1000 226195.2, 



and for olive oil, it is 



p" zz 28.2744 X 8 X915 zz 206968. 608 ; 



hence by summation, the entire pressure on the bottom, is 



P zz 3075802.3296 -f 226195.2 4. 206968.608 zz 3508966.1376, 



and lastly, dividing by 1728, we obtain 



172o 



The pressure which we have found in this last instance, is the very 

 same as that which would arise, if the vessel were filled with fluid of 

 a medium density ; for we have 



i (13598 4- 1000 + 915) zz 5171 medium density ; 



hence, the entire pressure on the bottom, is 



P 28.2744 X 24X5171 3508966.1376; 



which by division, gives 



3508966.1376 

 P - r^rr - zz 2030.6517 ounces, the same as before. 



182. Let the conditions of the problem remain as above, and let it 

 be required to determine the pressure on the concave surface of the 

 vessel, and to compare it with that upon the bottom. 



Let ABGH, as in the preceding case, represent an upright section 

 of the vessel, of which the base HG is parallel, and 

 the sides AH, BG perpendicular to the horizon; 

 and suppose the fluids of different densities to be 

 contained in the strata AC, DF and EG. 



Bisect the surface and base A B and HG, in the 

 points m and n, and join mn ; then do the centres 

 of gravity of the several cylindric surfaces occur in 

 that line. Draw the diagonals AC, DF and EG, 

 cutting the vertical line mn in the points c, b and a, which mark 

 the places of the respective centres of gravity. 



Put D zz AB or HG, the diameter of the vessel containing the fluids, 

 \d zz ea, the depth of the centre of gravity of the lower cylindric 



surface, 



\d' zz db, the depth of the middle cylindric surface, 

 <i"zz me, the depth of the upper cylindric surface ; each of these 



being referred to the surface of the respective fluid. 

 VOL. i. N 



