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OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



2. PRINCIPLES OF THE STABILITY OF FLOATING BODIES. 



PROBLEM LXI. 



455. A solid homogeneous body of uniform shape and dimen- 

 sions throughout the whole of its length, is placed upon a fluid 

 of greater specific gravity than itself, in such a manner, that the 

 centre of effort and the centre of buoyancy are in the same 

 vertical line. 



It is required to determine the stability, when by the 

 application of some external force, the body is deflected from 

 the upright position, or from a position of equilibrium through 

 u given angle. 



Let the solid to which our investigation refers be such, that the 

 vertical transverse sections perpendicular to the axis of motion, are 

 equal and similar trapezoids, as indicated by ABCD and abed in the 

 annexed diagrams. The solid floats upon the surface of the fluid IK, 



and ABCD is its position when in a state of equilibrium ; ABFE being 

 the extant portion of the vertical section, and EFCD the part immersed 

 beneath the fluid's surface. The point G is the centre of effort, or the 

 centre of gravity of the whole section, the plane of which is supposed 

 to pass through the centre of gravity of the body, and g is the centre 

 of buoyancy, or the centre of gravity of the part immersed below the 

 surface of the fluid ; then since the body floats in a state of equili- 

 brium, it follows from Proposition X., that PQ the axis of the section, 

 which passes through the points G and g, is perpendicular to EF the 

 line of floatation. 



