402 OF THE STABILITY OF STEAM SHIPS. 



excess of 34 feet ; but taking it at 34, the value of the stability for 

 a vessel in the form of a common parabola becomes 



s _ 34X0.25882 (1156 _ 1140t75)= 1M84; 



hence it appears, that the breadth at the water line, in the case of the 

 parabola, requires an increase of more than 6 feet, to give the same 

 stability as the triangle under the same depth and deflexion. 



494. If the equation for the stability in the case of the parabola, 

 be compared with that for the triangle, it will be seen that 3d 2 occurs 

 in the one case, instead of 2d 2 in the other ; consequently, the practical 

 rule as given for the triangle, will also apply to the parabola, if the 

 phrase " thrice the square of the corresponding depth" be substituted 

 for " twice the square," as it is now expressed ; the repetition of the 

 rule is therefore unnecessary. 



495. Again, if we put wnr3, then the transverse section of the 

 vessel is in the form of a cubic parabola, and the general equation 

 for the value of the stability becomes 



496. This form is greatly superior to the preceding one for a steam 

 vessel, as it gives the surfaces in contact with the water a less degree 

 of curvature ; but it requires a greater increase of the breadth at the 

 water line in proportion to the depth to obtain the same degree of 

 stability, which is manifest from the increase of the negative co- 

 efficient, the form of the equation being in every other respect the 

 same as before. 



The practical rule for this form, may be expressed in words at 

 length as follows. 



RULE. From the square of the breadth at the water line 

 when the vessel is upright, subtract 3.6 times the square 

 of the corresponding depth ; multiply the remainder by the 

 breadth drawn into the natural sine of the angle of inclina- 

 tion r and one twelfth of the product will express the stability. 



497. EXAMPLE. Let the breadth of the water line be 38 feet, and 

 let the depth and the deflexion, as well as the density of the vessel, 

 be the same as before ; what then will be the value of the stability ? 



Here by the rule we have 



(6 2 3.6d 9 )i=38 2 3.6 X19.5 2 =: 75.1 ; 



consequently, by multiplication and division, we have 



