78 OF THE PARALLELOGRAM AND ITS INSCRIBED PARABOLA. 



doubled, in which case it will have reference to the whole parabola, 

 and the pressure will be reduced to that upon its half, by employing 

 the constant \ instead of f- according to the rule, thus, 

 p = i x 32 x 40 2 X 62J = 640000 Ibs. 



91. If the axis of the semi-parabola were horizontal and its ordinate 

 vertical, as in the annexed diagram ; then, 

 the area of the semi-parabolic figure, as well 

 as that of its circumscribing parallelogram, 

 will remain the same, but the pressures 

 perpendicular to their respective surfaces 

 will be very different. 



Divide BD in n, in such a manner, that En and DW may be to one 

 another in the ratio of 5 to 3 ; and in like manner, divide CD in m, 

 so that cm and Dm shall be to each other in the ratio of 3 to 2. 



Through the points n and m, and parallel respectively to B F and 

 BD, draw the straight lines no, and ma, intersecting one another in 

 the point G, arid produce m G to E ; then , by the note to the pre- 

 ceding case, the point G is the centre of gravity of the semi-parabola 

 DCB, and EG is its perpendicular depth below BF, the horizontal 

 surface of the fluid. 



Therefore, let the preceding notation remain, and let the several 

 symbols refer to the same parts of the figure as in the preceding case, 

 disregarding the change of position which has taken place ; then, as 

 before, the area of the parallelogram BFCD, is 



A = 6/, 



and the pressure perpendicular to its surface, is 



For draw the diagonals B c and F D intersecting each other in the 

 point r, and through r draw rs parallel to BD or Em; then, r is the 

 centre of gravity of the rectangle BFCD, and sr its perpendicular 

 depth below BF the surface of the fluid; but according to our notation 

 srzr \b, and we have seen above, that A zz: bl; now, the pressure on 

 any surface, whatever may be its form, 



Is equal to the product that arises, when the area of the 

 surface pressed, is drawn into the perpendicular depth of its 

 centre of gravity, and again, into the specific gravity of the 

 fluid. 



Consequently, the pressure perpendicular to the surface of the 

 rectangular parallelogram BFCD, is 



