OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 363 



are parallel to one another, and the principal transverse section is that 

 which passes through the centre of effort. 



DEFINITION 7. The Axis of the Section, is the straight line which 

 passes through its centre of gravity, dividing it into two parts, which 

 in the case of a regular body are equal and similar to one another. 

 When this axis is vertical, it either coincides with, or is parallel to 

 the line of pressure. 



DEFINITION 8. The Line of Floatation, or The Water Line, is the 

 horizontal line in which the surface of the fluid meets a vertical trans- 

 verse section of the floating body. 



DEFINITION 9. The Plane of Floatation, is the horizontal plane 

 coincident with the surface of the fluid, and which passes through 

 the water line, dividing the body into the immersed and extant 

 portions. 



DEFINITION 10. The Equilibrating Lever, is a straight line equal 

 to the horizontal distance between the verticals passing through the 

 centre of effort and the centre of buoyancy ; or it is the horizontal 

 distance between the line of pressure and the line of support. 



DEFINITION 11. The Stability of Floating, or the Measure of 

 Stability, is that force by which a body floating on the surface of a 

 fluid, endeavours to restore itself, when it has been slightly inclined 

 from a position of equilibrium by the action of some external agent ; 

 or it is a force precisely equal to the fluid's pressure, or to the entire 

 weight of the floating body acting on the equilibrating lever. (See 

 Proposition (XI.) following). 



DEFINITION ]2. The Metacentre, is that point in which the axis 

 of the section and the line of support intersect each other ; it limits 

 the elevation of the centre of effort. 



Upon these definitions, therefore, in combination with the following 

 simple and obvious propositions, depends the whole doctrine of the 

 stability of floating bodies. 



PROPOSITION IX. 



451. It has already been admitted as a principle in the theory 

 of hydrostatics, that every body, whatever may be its form and 

 dimensions, if it floats upon the surface of a fluid of greater 

 specific gravity than itself, displaces a quantity of the fluid on 

 which it floats equal to its own weight, and consequently : 



