OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



361 



gravity of the body to be such, when compared with that of 

 the fluid on which it floats, as to sink it to the depth mn. The 

 body floats in equilibrio in the upright position ; suppose therefore 

 that by the application of some extraneous agent, it is deflected into 

 the position abed, where it is conceived to revolve about a horizontal 

 axis, passing through G its centre of gravity, at right angles to the 

 plane abed. If therefore, the body when thus inclined, requires the 

 force /'to retain it in that state, or to prevent it from returning to the 

 upright position ; then the equilibrium in which the body is originally 

 placed, is what we understand by the equilibrium of stability. 



Again, let the dotted Fig. 2. 



line in fig. 2 represent 

 a vertical section of 

 any uniform homogene- 

 ous prismatic body , float- 

 ing upright and quies- 

 cent on the surface of a 

 fluid, and let the specific 

 gravity of the solid be 

 such as to sink it in the 

 fluid to the depth mn\ 

 suppose now, that by the action of some external force, the body is 

 deflected from the vertical position into that represented, by a b cd ; it 

 is obvious, that the revolution is made about the horizontal axis 

 passing through G the centre of gravity, at right angles to the plane 

 abed. 



Hence, if the body when thus inclined, requires the application of 

 the force/ to retain it in that state, or to prevent it from inclining 

 further ; then the equilibrium in which the body is originally placed, 

 is what we comprehend by the equilibrium of instability . 



Finally, let abed, fig. 3, be the vertical -* 3- 



section, and let the specific gravity of the 

 body be such, as to sink it to the depth md; 

 the solid floats in equilibrio in the upright 

 position, and in such a manner, that an 

 evanescent force will either retain it in that 

 state, or deflect it from it ; this is the insen- 

 sible equilibrium, or the equilibrium of indif- 

 ference, and the solid is said to overset. 



449. Of these three species of equilibrium, bodies floating on the 

 surface of a fluid are manifestly susceptible; but they admit of a 



