360 



OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



continues to decrease until it vanishes, in which case the body settles 

 in another situation, which also satisfies the conditions of equilibrium. 



Again, a solid body may be so constituted with respect to shape 

 and dimensions, that in every position which can be given to it on 

 the surface of a fluid, it will rest in a state of equilibrium ; for in all 

 situations and under every condition, the centre of gravity of the 

 whole body and that of the immersed part, will occur in the same 

 vertical line ; this being the case, it is manifest that in such a body, 

 the equilibrium cannot be disturbed, because the external force, how- 

 ever it may be applied, can only operate to turn the solid round an 

 axis, passing through the centre of gravity in a direction parallel to 

 the horizon. 



Homogeneous spheres are bodies of this sort, so also are homo- 

 geneous cylinders floating with the axis horizontal; these have no 

 tendency to solicit one situation in preference to another, and con- 

 sequently, in whatsoever position they are placed, with reference to 

 the axis of revolution, they are still in a state to satisfy the conditions 

 of equilibrium, for the centre of gravity of the whole body and that 

 of the immersed part, are always situated in the same vertical line. 



In the first case then, where the body has a tendency to restore 

 itself to the original position, the equilibrium is said to be stable ; in 

 the second case, where the body deviates farther and farther from the 

 original state, the equilibrium is unstable ; and lastly, in the case where 

 the body has no tendency to remain in, or to solicit one position in 

 preference to another, the equilibrium is said to be insensible. 



448. The conditions of equilibrium as here stated, are in themselves 

 sufficiently simple and explicit, but in order that none of our readers 

 may enter upon this important and difficult subject, with incorrect 

 notions respecting the different species of equilibrium, and the various 

 conditions or circumstances of floating under which a body may be 

 placed, we have thought it expedient to subjoin the following expo- 



sitions and illustra- 

 tions. 



Let the dotted line 

 inj^. 1 represent a 

 transverse section of 

 any uniform prismatic 

 body, placed verti- 

 cally on the surface 

 of a fluid, and sup- 

 pose the specific 



Ffe.i. 



