ON HYDROSTATICS. 267 



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 tlie 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 -rW 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 com- 

 bined with others which take place in a transverse direction: a ship, for ex- 

 ample, may roll on an axis in the direction of her length, and may heel, 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 equivalent 

 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 esti- 

 mated by the weight of a portion of the fluid equal in bulk to the solid. 



