364 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



The specific gravity of the supporting fluid, is to that of 

 the floating body, as the whole magnitude of the solid is to 

 that of the part immersed. (See Proposition VII.) 



PROPOSITION X. 



452. If a solid body, of whatever form or dimensions, floats 

 upon the surface of a fluid of greater specific gravity than itself: 



It is impelled downwards by its own weight acting in the 

 direction of a vertical line passing through the centre of 

 effort ; and it is propelled upwards by the pressure of the 

 fluid which supports it acting in the direction of a vertical 

 line passing through the centre of buoyancy. (See Proposi- 

 tion VI.) 



Therefore, if these two lines are not coincident, the floating body 

 thus impelled must revolve upon an axis of motion, until it attains a 

 position in which the centre of effort and the centre of buoyancy are 

 in the same vertical line. 



PROPOSITION XL 



453. If a solid body of any particular form and dimensions, 

 floating on the surface of a fluid of greater specific gravity than 

 itself, be deflected from the upright position through a given 

 angle : 



The stability of the body is proportional to the length of 

 the equilibrating lever, or to the horizontal distance between 

 the vertical lines passing through the centre of effort and the 

 centre of buoyancy. (See Problem LXI. following.) 



When the horizontal distance here alluded to is equal to nothing ; 

 that is, when the centre of effort and the centre of buoyancy are 

 situated in the same vertical line; then the stability, or the force 

 which urges the body round its axis of motion vanishes, and the equi- 

 librium is that of indifference ; for in this case, the metacentre coin- 

 cides with the centre of effort. 



If the floating body be any how inclined from the upright position, 

 and if, in consequence of the inclination, the line of support falls on 

 the same side of the centre of effort as the depressed parts of the 

 solid, then the length of the equilibrating lever is accounted positive, 



