OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 397 



119384 : 27.32 : : 18510.97 : 4.25 feet, 



483. But in order to infer the stability of the vessel from the value 

 of gt just discovered, it is necessary to have given the distance eg, or 

 the distance between the centre of effort and the centre of buoyancy ; 

 now it is obvious, that the position of this latter point is regulated 

 entirely by the form and dimensions of the immersed portion of the 

 vessel, and consequently, it may be considered as absolutely fixed 

 with respect to the plane of floatation ; but since the position of the 

 centre of effort is regulated partly by the construction and equipment, 

 and partly by the distribution of the loading and ballast, it can only 

 be assumed on the ground of supposition, unless in cases where the 

 position of that point has been actually ascertained by accurate 

 mensuration. 



In several instances, the distance Gg has been measured, and found 

 to be equal to about one eighth of the greatest breadth at the plane 

 of floatation ; therefore, by assuming this to be the case generally, we 

 have 



eg == J- of 43.16 = 5.396 feet, 



therefore, by Plane Trigonometry, it is 



rad. : 5.396 : : sin. 30 : gs, 

 from which, by reducing the proportion, we obtain 



#5 = 2.698 feet, 

 which being subtracted from g t, the remainder is 



S=:GZ = 4.25 2.698=:1.552 feet, the measure of 

 the vessel's stability, or the length of the equilibrating lever. But the 

 whole weight of the vessel, as found from the solidity of the immersed 

 part, is 



119384 



w nr 341 1 tons very nearly ; 35 cubic feet 



35 



of sea water being equal to one ton weight ; consequently, the 

 momentum of the redressing force, or the power which the pressure 

 of the water exerts to restore the vessel to the upright position, is 

 equal to 3411 tons acting on a lever whose length is 1.552 feet; or 

 it is equivalent to a force or pressure of 245 tons acting at the dis- 

 tance of half the greatest breadth of the vessel from the axis ; for by 

 the principles of the lever, it is 



21.58 : 3411 : : 1.552 : 245 tons nearly. 



The preceding is the method of determining the stability of a ship, 

 on the supposition that the data are all assignable ; the process con- 



