258 OF THE EQUILIBRIUM OF FLOATATION. 



s' n: the specific gravity of the fluid, and 

 w/iz: the weight of a quantity of the fluid, of the same magni- 

 tude as that part of the body which falls below the 

 plane of floatation ; then, according to the above in- 

 ference just stated, we get 



w~w. 



But because the weight of any body is expressed by the product of 

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



w ms, and w' m's', 

 consequently, by comparison, we have 



ms = m's'. (200). 



Therefore, if this equation be converted into an analogy, the truth 

 of the Proposition will become manifest ; for 



m : m' : : s' : s, 



being precisely the principle which the Proposition implies. 

 From the principle demonstrated above, various curious and inte- 

 resting questions may be resolved, and by selecting a few which point 

 directly to practical subjects, the information afforded by their reso- 

 lution will sufficiently repay the labour of an attentive perusal. 



312. EXAMPLE I. A cubical block of fir, whose specific gravity is 

 0.55, floats in equilibrio on the surface of a fluid whose specific gravity 

 is 1.026 ; how much of the block is above, and how much below the 

 plane of floatation, the entire magnitude being equal to 512 cubic 

 inches ? 



Here, by the Proposition, we have 



512 : m' : : 1.026 : 0.55, 



and from this, by equating the products of the extreme and mean 

 terms, we get 



1.026m' zz 281.6, 

 and finally, dividing by 1.026, we obtain 



m'zz ' m 274. 464 cubic inches. 



It therefore appears, that the quantity of the solid immersed below 

 the plane of floatation, is 274.464 cubic inches ; consequently, the 

 part extant is 512 274.464 = 237.536 cubic inches, being less than 

 half the magnitude of the body, by 18.464 cubic inches. 



313. EXAMPLE 2. Let the specific gravities and the magnitude of 

 the body remain as in the last example ; what weight must be added 



