OF THE EQUILIBRIUM OF FLOATATION. 275 



tively IK and GH, GH being the surface 

 of contact of the two fluids. 



Put m =: A BCD, the magnitude of the 



whole body, 



x m ABCFE, the magnitude of the 

 part immersed in the lighter 

 fluid, and 

 m a; rr EFC D, the magnitude of the part immersed in the heavier 



fluid. 



Therefore, if the specific gravities of the body and the fluids be 

 respectively denoted by s", s and s', as in the Proposition; then, we 

 shall have 



ms"=:xs-\- (m x)s', 



from which, by transposition, we obtain 



x (s' 5) zz m(s' s"), 

 and finally, by division, it becomes 



_ 



'' 



341. An equation of an extremely simple and convenient form, from 

 which we deduce the following practical rule. 



RULE. Multiply the magnitude of the immersed solid by 

 the difference between its specific gravity and that of the 

 heavier Jluid; then divide the product by the difference between 

 the specific gravities of the fluids, and the quotient will give 

 the magnitude of the part immersed in the lighter Jluid. 



342. EXAMPLE. A cubical piece of oak containing 2000 inches, 

 and whose specific gravity is 0,872, that of water being unity, floats 

 in equilibrio between two fluids, whose specific gravities are respec- 

 tively 1.24 and 0.716 ; what portion of the solid is immersed in each 

 of the fluids, supposing them to be altogether unmixable ? 



The operation being performed according to the rule, will stand as 

 below. 



2000(1.24 0.872) 



(1.^4-0.716)- 14 4 ' 58 ublC mches ' 



This result expresses the solid contents of that part of the body 

 which is immersed in the lighter fluid ; consequently, the part which 

 is immersed in the heavier fluid, is 



2000 1404.58 = 595,42 cubic inches. 

 T 2 



