202 LECTURE XXI. 



metacentve, or centre of pressure, which may be considered as a fixed point 

 of suspension or support, for the solid body. It is obvious that when the 

 lower surface of the body is spherical or cylindrical, the metacentre must 

 coincide with the centre of the figure, since the height of this point, as well 

 as the form of the portion of the fluid displaced, must remain invariable in 

 all circumstances, and the nature of the equilibrium will depend on the 

 distance of the centre of gravity above or below the centre of the sphere or 

 cylinder. And the place of the metacentre may always be determined 

 from the form and extent of the surface of the displaced portion of the 

 fluid, compared with its bulk and with the situation of its centre of gravity. 

 For example, if a rectangular beam be floating on its flat surface, the 

 height of the metacentre above the centre of gravity will be to the breadth 

 of the beam, as the breadth to twelve times the depth of the part immersed. 

 Hence, if the beam be square, it will float securely when either the part 

 immersed or the part above the surface is less than T Vo- of the whole ; but 

 when it is less unequally divided by the surface of the fluid, it will overset. 

 If, however, the breadth be so increased as to be nearly one fourth greater 

 than the depth, it will possess a certain degree of stability whatever its 

 density may be. (Plate XIX. Fig. 247.) 



When the equilibrium of a floating body is stable, it may oscillate back- 

 wards and forwards in the neighbourhood of the quiescent position : and 

 the oscillations will be the more rapid in proportion as the stability is 

 greater in comparison with the bulk of the body. Such oscillations may 

 also be combined with others which take place in a transverse direction : a 

 ship, for example, may roll on an axis in the direction of her length, and 

 may pitch, at the same time, upon a second axis in the direction of the 

 beams. Besides these rotatory vibrations, a floating body which is suffered 

 to fall into a fluid, will commonly rise and sink several times by its own 

 weight ; and in all these cases, the vibrations of any one kind, when they 

 are small, are performed nearly in equal times : but various and intricate 

 combinations may sometimes arise, from the difference of the times in 

 which the vibrations of different kinds are performed. 



When a solid body is wholly immersed in a fluid, and is retained in its 

 situation by an external force, it loses as much of its weight as is equiva- 

 lent to an equal bulk of the fluid. For, conceiving the fluid which is 

 displaced by the body, to have been converted into a solid by congelation, 

 it is obvious that it would retain its situation, and the difference of the 

 pressures of the fluid on its various parts would be exactly sufficient to 

 support its weight. But these pressures will be the same if a body of any 

 other kind be substituted for the congealed fluid ; their buoyant effect may, 

 therefore, be always estimated by the weight of a portion of the fluid equal 

 in bulk to the solid. Thus, when a little figure, containing a bubble of air, 

 is immersed in a jar of water, which is so covered by a bladder that it may 

 be compressed by the hand, the bulk of the figure with its bubble is 

 diminished by the pressure, it is, therefore, less supported by the water, and 

 it begins to sink ; and when the hand is removed it immediately rises 

 again. (Plate XIX. Fig. 248.) 



While a body is actually rising or sinking in a fluid, with an accelerated 



