Equilibrium of Floating Bodies. 331 



The ice-bergs that float from the polar seas down into warm- 

 er regions, are gradually dissolved, not only by the sun's rays, 

 but also by the currents of warm air and warm water to which 

 they ate exposed. But these causes operate more powerfully on 

 the sides than upon the top and botto;n, and their horizontal dimen- 

 sions are thus reduced faster than their vertical, whereby they 

 become unstable, and are overturned. Being still subject to 

 the same kind of influence, they are liable to repeated and fre- 

 quent changes of position before they are completely wasted. 



443. To investigate generally the conditions of equilibrium F . g 

 of a floating body, let HsilF represent a vertical section, the 

 point G of the principal axis ANF being the centre of gravity 

 of the whole, and the point B the centre of buoyancy. The 

 solid being inclined a little, the water line HNI shifts to H'NF, 

 and the centre of buoyancy B to B'. From what has been said, 

 it will be perceived that the area of HFI is to the sum of the 

 two triangles Nil', HNH', as NP is to BB' ; that is, 



44<>i 



area HFI : NI X IF : : f JV7 : B&, 

 but the triangles INI', BMB', being similar, 

 IF : JV7 : : BB 1 : BM, 



therefore, by multiplying the terms in order, and suppressing the 

 common factor in each of the ratios, we have 



area HFI : JV7 : : f JV7 : BM, 

 or, calling the area HFI, <*, and the length of the water line } HNI, ? 



tf : Q a) 2 :: ia : BM = 



Accordingly, the equilibrium will be stable when the cube of the 

 length of the water-line JV7, divided by 12 times the area of the 

 section, exceeds the interval BG between the centre of gravity 

 and that of buoyancy. If this quotient be just equal to BG, the 

 equilibrium will be that of indifference ; and lastly, when this 

 quotient is less than BG, the equilibrium will be unstable, and 

 the body will be liable upon a slight inclination to overset. 



