326 Hydrostatics. 



in the fluid, the portion displaced will be greater and greater, 

 and, consequently the buoyant effort will increase, till at length 

 it will become equal to the weight of the body. The point G 

 will still continue to move on in the same direction by virtue of 

 its acquired velocity, but then the buoyancy of the fluid exceed- 

 ing the weight of the body, its velocity will be retarded contin- 

 ually, till finally the downward motion of G will cease, and then it 

 will begin to return toward its first position, arid thus it will continue 

 to oscillate till the motion is entirely destroyed by the resistance 

 of the fluid. The extent of these oscillations will be smaller, ac- 

 cording to the difference at the outset between the weight of the 

 body and that of the fluid displaced, compared with the weight 

 of the body. If the body be but little removed from its position, 

 of equilibrium, this difference will be small, the extent of the 

 oscillations will consequently be small, and will not materially 

 affect the stability of the body. 



443. During these oscillations of the point G, the body will 

 turn about this centre, in precisely the same manner as if it were 

 137. fixed ; its motion of rotation will be produced, therefore, by the 

 buoyancy of the fluid, which acts at the point M according to 

 the direction JI/Z; and its state of equilibrium will be stable or 

 unstable, according as the straight line GB tends to approach to, 

 or recede from, the vertical. Now it is evident from inspection, 

 that the buoyancy of the fluid will tend to restore the straight 

 line GB to its vertical position, whenever the point M is above 

 the point G ; on the other hand, if M or the metacentre is below 

 the point G, as at JW, for instance, the buoyancy of the fluid, 

 which will then be exerted according to M'Z', will cause the 

 straight line GB to depart further from a vertical position, and 

 tend to upset the floating body. Therefore, when the metacen- 

 tre is below the centre of gravity, the equilibrium is unstable ; 

 and, on the other hand, when the metacentre is above the centre 

 of gravity, the equilibrium is stable ; at least with respect to all 

 positions in which the plane HFI continues vertical. If, in a 

 particular case, the metacentre coincides with the centre of grav- 

 ity, there will be no tendency to turn one way or the other, and 

 the straight line GB will remain stationary, whatever inclination 

 be given to it. 



