CHAPTER XL 



OF THE EQUILIBRIUM OF FLOATATION. 



BY the equilibrium of floatation is generally meant the position of a floating body^ 

 when its centre of gravity is in the same vertical line with the centre of gravity of 

 the displaced fluid. When the lower surface of the floating body is spherical or 

 cylindrical, the centre will coincide with the centre of the figure ; as, in all circum- 

 stances, the height of this point, as well as the form of the volume of fluid displaced, 

 must remain invariable. In the next proposition, we shall prove, that the place of 

 the centre is determined by the doctrine of forces combined with the elementary 

 principles of hydrostatics, by considering 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. Our inquiry will be found to embrace also rectangular figures ; 

 solids in the form of paraboloids and cylinders, together with the equilibrium of 

 floatation of solids immersed in fluids of different specific gravities ; the theory of 

 construction of the aerometer ; the hydrostatic balance, and the method of weighing 

 solid bodies in fluids. The reader will therefore consider this syllabus as the 

 paraphrase of a definition for the term equilibrium of floatation. 



PROPOSITION VI. 



307. When a body floats in a state of equilibrium on the 

 surface of an incompressible and non-elastic fluid : 



The centre of gravity of the whole body, and that of the 

 part immersed ; or which is the same thing, that of the fluid 

 displaced, must occur in the same vertical line* 



Let ADBH be a vertical section passing through G and g, the centres 

 of gravity of the whole body AHBD; and of the immersed part A DB, 

 which falls below EF the plane of floatation. 



* The vertical line, which passes through the centres of gravity of the whole 

 body, and the part immersed beneath the plane of floatation, is generally denomi- 

 nated the line of support. 



