280 



OF THE EQUILIBRIUM OF FLOATATION. 



therefore, by equating the products of the extreme and mean terms 

 and casting out the common quantity m, we obtain 

 m"(s"s) _ m's" 



s' sY~ : ~7"' 

 by clearing the equation of fractions, we get 



m"s'(s" s) = nf8 l! (S s), 

 and finally, by division, we have 



'(" ) (219). 



351. Now, it is manifest, that in order to determine from this 

 equation, what part of the body is immersed in the water when it 

 floats in vacuo, it is necessary in the first place, to ascertain how 

 much of it is immersed when the floatation occurs in air : Equation 

 (217) determines this, and the practical rule deduced from the equa- 

 tions (217) and (219) may be expressed in words at length in the 

 following manner. 



RULE. From the specific gravity of the floating body, sub- 

 tract the specific gravity of air ; multiply the remainder by 

 the magnitude of the body, and divide the product by the 

 difference between the specific gravities of water and air, for 

 the part which is immersed in water, when the incumbent fluid 

 is air. 



Again. Multiply the difference between the specific gravities 

 of water and air by the specific gravity of the floating body ; 

 divide the product by the difference between the specific gra- 

 vities of the solid body and air, drawn into the specific gravity 

 of water ; then, multiply the quotient by the magnitude of the 

 part immersed in water when the body floats in air, and the 

 product will be the magnitude of the part immersed in water, 

 when the body floats in vacuo. 



352. EXAMPLE. A mass of oak whose specific gravity is 0.925, con- 

 tains 185 cubic inches; what quantity of it exists below the plane of 

 floatation, supposing it to float on water in vacuo, the specific gravity 

 of the air being 0.0012 at the instant of observation ? 



By operating according to the directions given in the first clause of 

 the rule, the quantity below the plane of floatation when the incumbent 

 fluid is air, becomes 



185(0.925 0.0012) 



m =. : - 171.108 cubic inches; 



(10.0012) 



