270 OF THE EQUILIBRIUM OF FLOATATION. 



which being reduced, gives 



x 1/8"H 8- /oim 



Y 1.5708j9s (210). 



331. And the practical rule for reducing this equation, may be 

 expressed in words at length, as follows. 



RULE. Divide the weight which disturbs the equilibrium, 

 by 1.5708 times the parameter of the generating parabola, 

 drawn into the specific gravity of the fluid, and to the quotient 

 add the square of the distance between the vertex of the figure 

 and the plane of floatation in the first position of equilibrium ; 

 then, from the square root of the sum, subtract the said dis- 

 tance, and the remainder will express the quantity of descent. 



332. EXAMPLE. A solid body in the form of a paraboloid, floats on 

 a vessel of water in a state of equilibrium with its vertex downwards, 

 when 12 inches of the axis are immersed below the plane of floata- 

 tion ; how much farther will the body sink, supposing a weight of 

 28 Ibs. to be laid on its base, the parameter of the generating parabola 

 being 16 inches? 



Here, by pursuing the directions of the rule, we get, 



90 



12 2 H 12 =z 1.22 inches. 



1.5708X16X. 03617 



333. If the weight w should be subtracted from the paraboloid 

 instead of being added to it, the quantity of ascent will then be deter- 

 mined by equation (209), where we have 



divide both sides of this equation by the quantity 1.5708p5, and we 

 shall obtain 



1.5708ps J 

 which, by transposing the terms, becomes 



By completing the square, we get 



