332 Hydrostatics. 



Whatever be the figure of the section HFI, its area and con- 

 sequently the centre of gravity and that of buoyancy may be 

 found to any required degree of exactness by the method of 

 article 114. 



Although the above formula has reference only to a single 

 lamina, and to motion in the plane of this lamina, it is still ap- 

 plicable to any solid whose parallel sections are equal and sim- 

 ilar, for in this case the whole may be considered with respect 

 to motion in a parallel plane, as concentrated in the middle sec- 

 tion or lamina represented by HFI ; and with respect to motion 

 in a vertical plane perpendicular to the lamina, by supposing a 

 corresponding section, and putting & equal to the area of this 

 section, and a' equal to the length of the water-line, we shall 

 have the same formula to express the conditions of equilibrium 

 as before. 



When the sections or laminae are unequal, we find the height 



of the metacentre of each lamina, and multiply it by the bulk of 



this lamina, and then divide the sum of the products, or moments 



of the several lamina?, by the sum of the laminas for the height 



w - of the common metacentre. 



449. In the case of a merchant ship, it will furnish a tolera- 

 ble approximation to take the section near the prow where the 

 girth is commonly the largest. The transverse section of the hull 

 of a ship is not materially different from the form of a parabola. 

 Therefore, on this supposition, the height of the metacentre above 



Fi 219 ^ e centre f buoyancy, or BM, is equal to the cube of ///, the 

 length of the water-line, divided by twelve times the area of 



Cal. 94.HFL But the area HFI is equal to f HI X JVT. Hence, 



, 



12 tf " 12xi#/XAT 8 AT 2 AT' 



f " ' ' ' ' - - - " '- ' ' ' " ' " ' - - iiu - 



t Where great accuracy is required, the following formula may 

 be used j namely, 



