272 



OF THE EQUILIBRIUM OF FLOATATION. 



rv' rr the added weight, 

 n>" the weight of the fluid displaced, 

 s =z the specific gravity of the fluid, and 

 s' = the specific gravity of the floating solid. 



Then, because the absolute weight of any body, is expressed by its 

 magnitude drawn into its specific gravity ; it follows, that the weight 

 of the floating solid, is 



w ms', 



and in like manner, the weight of the displaced fluid, is 

 n" m s ; 



now, it is manifest, from the nature of the problem, that the weight 

 of the displaced fluid is equal to the weight of the floating body, 

 together with the superadded weight; consequently, we have 



/ -J- rv ~w' -f- w/wis ; 

 from which, by transposition, we obtain 



w'=ffi(* '). .. (212). 



337. The practical rule for the reduction of this equation is very 

 simple : it may be expressed as follows. 



RULE. Multiply the difference between the specific gravities 

 of the fluid and the floating solid, by the whole magnitude of 

 the floating body t and the product will express the value of 

 the added iveight. 



338. EXAMPLE. A mass of oak, whose specific gravity is .872, that 

 of water being unity, floats in equilibrio on the surface of a fluid 

 whose specific gravity is 1.038 ; what weight applied externally to the 

 floating body, will depress it to the level of the fluid surface, sup- 

 posing the magnitude of the body to be equal to 8 cubic feet ? 



Here, by operating as the rule directs, we shall have 

 w' 8(1.038 .872) 1.328 cubic feet of water ; 



but it is a well known fact, that one cubic foot of water weighs 62 

 Ibs. avoirdupois, very nearly ; consequently, we have 



wf=1.328X62J = 831bs. 



PROPOSITION VIII. 



339. If a solid body, which is specifically heavier than one of 

 two fluids which do not mix, and specifically lighter than the 

 other, be immersed in the fluids : 



