278 OF THE EQUILIBRIUM OF FLOATATION. 



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

 half the difference between the given specific gravities, and the 

 remainder will be the specific gravity of the solid body. 



348. EXAMPLE. Let the specific gravities of the fluids remain as 

 above ; what must be the specific gravity of the body, so, that when 

 it is in a state of equilibrium, one half of it may be immersed in each 

 solid ? 



One half the difference of the given specific gravities, is 



(1.24 0.716) =0.262; 

 consequently, by subtraction, we have 



a- =1.24 0.262 = 0.978, and with this specific 

 gravity, a body, whatever may be its magnitude, will be equally 

 immersed in the two unmixable fluids. 



349. If the specific gravity of the lighter fluid vanish, or become 

 equal to nothing; then equation (215) becomes 



and by converting this equation into an analogy, we get 

 m : m' : : s 1 : s". 



This analogy expresses the identical principle, which is announced 

 and demonstrated in Proposition VII. preceding ; it is therefore pre- 

 sumed, that the examples already given will be found sufficient to 

 illustrate the application of this very elegant and important property. 

 Since the magnitude of the whole floating body is equal to the sum 

 of its constituent parts, it follows, that according to our notation, 



m = m' 4~ m " '* 

 consequently, by substitution, equation (215) becomes 



(m 4- m") s" = m' s' 4- m" s, 

 or by transposing and collecting the terms, we get 



m ("-) = '(*-*"), 

 and by converting this equation into an analogy, we obtain 



m : m" ::( s " s) : (s's). 



By comparing the terms of the proportion as they now stand, it 

 will readily appear, that if the specific gravity of the lighter fluid be 

 increased, the term (s" s) is diminished, while (s' s") remains the 

 same ; consequently, the first term ni will be diminished with respect 

 to the second term m" ; which implies, that the part of the body in 

 the lighter fluid will be increased ; hence arises the following very 

 curious property, that 



