454 NOTES. 



to the width of its section or water lines. We have a curious proof of this in the 

 construction of the French ship of the line, of 74 guns, called Le Scipion, fitted for 

 sea at Rochfort, in 1779; but she wanted stability, which, after various fruitless 

 attempts, was achieved by applying a bandage or sheathing of light wood to the 

 exterior sides of the vessel. This cushion, bandage, or sheathing, was from one 

 foot to four inches in thickness, extending throughout the whole length of the 

 water line, and ten feet beneath that line. We are left to infer Le Scipion then 

 floated with permanent stability. 



If the centre of buoyancy stand higher than the centre of gravity, the floating 

 body will, in every declination maintain its stability, and regain its perpendicular 

 position ; for though made to lean towards either side, the vertical pressure exerted 

 against that variable point will soon bring it back again into the line of support. 

 But the elevation of the centre of buoyancy above that of gravity, is by no means 

 an essential requisite to the stability of floatation; on the contrary, it falls in most 

 cases considerably below the centre of gravity about which the body rolls. The 

 buoyant efforts may be considered as acting upon any point in the vertical line, 

 and consequently, as united in the point where the line crosses the axis of the 

 floating body. If the point of concourse, thus assigned, should stand above the 

 centre of gravity, the body will float firmly, and will right itself after any small 

 derangement. If it coincide with the centre of gravity of the homogeneous body, 

 this will continue indifferent with regard to position; but if the vertical line 

 should meet the axis below the centre of gravity, the body will be pushed forwards, 

 its declination always increasing till it finally oversets. 



Thus, a sphere of uniform consistence floated in water, will sink till the weight 

 of the fluid displaced by the immersed portion shall be equal to its own load. The 

 centre of gravity of this body is the centre of the sphere itself; but the centre of 

 buoyaney must be the centre of gravity of the volume of immersion, which there- 

 fore lies below the centre of gravity of the body, in an axis perpendicular to the 

 water line, or line of floatation. The ball is hence pressed down by its own 

 weight collected in its centre of gravity, and pushed up in the opposite direction by 

 an equal force combined in the centre of buoyancy ; both of the forces, however, 

 concurring in the centre of gravity of the immersed sphere. Wherefore, being 

 always held in equilibrium by those antagonist forces, it will remain still in any 

 position which it may happen to occupy. But this indifference to floating will 

 obtain only when the sphere is perfectly homogeneous, and its centre of gravity 

 coincides with the centre of magnitude, for otherwise, the former descending as 

 low as possible, would always assume a determinate position. 



A cylinder will, according to its density, and the proportion of its diameter and 

 altitude, exhibit the three features of a floating body, in indifference, instability, or 

 permanence of equilibrium. For example, a cylinder, the specific gravity of which 

 is to that of the fluid in which it floats, as 3 to 4, its axis being to the diameter of 

 the base as 2 to 1, if placed on the fluid with its axis vertical^ will sink to a depth 

 equal to a diameter and a half of the base ; and as long as the axis is sustained in 

 a vertical position by external force,, the centre of gravity of the solid and the 

 centre of the immersed part will be situated in the same vertical line ; but the solid 

 will not float permanently in that position, for as soon as the external force is 

 removed, it will overset and float with its axis horizontal. But a cylinder whose 

 axis is one half, instead of twice the diameter of the base, being placed in a fluid 

 with its axis vertical, will sink to the depth of three fourths of a diameter^ and will 



