268 OF THE EQUILIBRIUM OF FLOATATION. 



w zr the weight which is added to or subtracted from the 



cylinder, and 



5 z= the specific gravity of the fluid. 



Then, by the principles of mensuration, the solidity of the cylinder, 

 of which the section is IKFE or EF&O, becomes 



and the weight of an equal magnitude of the fluid, is 



m s = 3.l4l6r*sx', 



but this, by the nature of equilibrium, is equal to the disturbing 

 weight ; hence we have 



w=3.Ul6r*sx, 

 and from this, by division, we obtain 



~3.1416rV (207). 



328. The practical rule for reducing this equation is very simple ; 

 it may be expressed in words at length in the following manner. 



RULE. Divide the given disturbing weight, whether it be 

 added to or subtracted from the cylinder, by the area of the 

 horizontal section, drawn into the speci/ic gravity of the fluid, 

 and the quotient mill express the quantity of descent or ascent 

 accordingly. 



329. EXAMPLE. A cylinder of wood, whose diameter is 24 inches, 

 floats in equilibrio with its axis vertical, on the surface of a fluid 

 whose specific gravity is expressed by unity ; now, supposing the 

 equilibrium to be destroyed by the addition or subtraction of another 

 body, of which the weight is 56 Ibs. ; through what space will the 

 body move before the equilibrium be restored ? 



Here, by proceeding as directed in the rule, we have 



_ 56 



a '~~3.1416xl2 2 X.03617*~~ 3 ' 42 



Again, if the body should be in the 

 form of a paraboloid, floating in equi- 

 librio on the surface of a fluid with its ~~ 

 vertex downwards, as represented in the xj 

 annexed diagram, where ACB is a ver- 

 tical section passing along the axis CD, 

 and GH the surface of the fluid on 



* The decimal fraction 0.03617 expresses the weight in Ibs. of a cubic inch of water. 



