| HYDROSTATICS 435 
and parallel to the surface of the liquid. ¢ is in the line which bisects 
_ the horizontal sides of the rectangle or parallelogram. 
Sh? + Bhd +d? ox pollen % 
i ). If h=0, = 24. 
Fig. 709. A triangle with its base below and parallel to the surface 
B= 3 
a a —————— 
ae = ’ == 
'% 
rar, 
' 
b teh 
+. 1 
Fia. 708. Fia@. 709. Fiq. 710. Fig. 711. 
of the liquid, the vertex being below the base. c¢ is in the line joining 
ane vertex and the middle point of the base. 
6h? + es +d? z 
_ Fig. 710. A triangle wi its base parallel to the surface of the 
liquid, the vertex being above the base and below the surface of the 
liquid. is in the line joining the vertex with the middle point of the 
base. 
B= 
_ 6h? + Bhd + 3d? 
Gh+4d 
Fig. 711. A circle entirely immersed, its centre being at a distance 
h from the surface of the liquid. 
a 
Baz h+ re If h= %= $d. 
370. Resultant Pressure on a 2 Immersed in a Liquid.—It is 
evident that the horizontal components of the pressures on the surface 
of the immersed body balance one another, there being no tendency to 
_ move the body horizontally, and the resultant pressure must therefore act 
If h=0, #=$d. 
Suppose the body to be divided into a large number of vertical prisms, 
of which AB (Fig. 712), having a horizontal sectional area a,isone. Let 
the upper end of AB be at a depth h,, and the lower 
end at a depth h, below the free surface of the liquid, 
and let w be the weight of a unit of volume of the liquid. 
The downward force exerted by the liquid on the top of 
AB is wah,, and the upward force exerted by the liquid 
on the bottom of AB is wah,. Hence the resultant 
upward force on AB is wah, — —h,), and this is the 
weight of a volume of liquid ‘equal to the volume of yg, 719, 
AB. This result will be true for each of the prisms 
_ into which the body is divided ; hence the resultant pressure of the liquid 
on the body is an upward force equal to the weight of a volume of the 
liquid equal to the volume of the body. 
_ Stating the foregoing result in another way: if the body is weighed 
