OF THE EQUILIBRIUM OF FLOATATION. 259 



to the body, in order that its upper surface may be made to coincide 

 with that of the fluid ? 



Put x nz the weight which must be added to the solid, in order that 

 it may sink to a level with the surface of the water ; then, we have 



m: m + x :: 0.55 : 1.026, 

 and by equating the products of the extremes and means, we get 



0.55 (m + x) = 1.026m; 

 therefore, by transposition, we obtain 



0.55* = 0.476m; 

 but according to the question, mzr:512 cubic inches, hence we get 



0.55*:= 243.712, 

 and finally, by division, we have 



243 712 

 x zn - - 443.1 13 cubic inches; but a 



cubic inch of fir of the given specific gravity, weighs 0.0198 Ibs. 

 avoirdupois, very nearly ; consequently, the weight to be added for 

 the purpose of making the solid sink to the same level as the surface 

 of the fluid, is 



.0198X443.113 8.774 Ibs. nearly. 



314. But to determine generally, the magnitude which must be 

 added to the original solid, in order that its surface maybe coincident 

 with that of the fluid :- Let zziithe weight to be added; then, by 

 the Proposition, we have 



m -{- x : m : : s : s, 



from which, by equating the products of the extremes and means, 

 we get 



s (m -\- x) s' m, 



and by separating the terms, it becomes 



^m -\- sx^ns'm, 



and finally, by transposition and division, we obtain 

 _m(s' s) 



s (201). 



Therefore, the practical method of reducing this equation, may be 

 expressed in words in the following manner. 



RULE. From the specific gravity of the fluid, subtract that 

 of the solid ; then, multiply the remainder by the magnitude 

 of the solid, and divide the product by its specific gravity for 

 the weight to be added. 



s2 



