404 OF THE STABILITY OF STEAM SHIPS. 



500. But we must now proceed to consider the second variety, in 

 which the ordinates are parallel to the breadth of the vessel at the 

 water line when the vessel is placed in an upright and quiescent 

 position ; and in this case, the general equation expressing the value 

 of the stability, is 



^sin^x .12nd 2 \ 



"ITA 6 ~n*+3rc + 2/' (295). 



where the several letters which enter the equation indicate precisely 

 the same quantities, and refer to the same parts of the vessel as before ; 

 and by giving particular values to the quantity n, we shall obtain 

 another series of equations, indicating the stability according to the 

 order of the parabolic curve by which the vessel is bounded. 



501. If we put w:nl, then the transverse section of the vessel 

 becomes a triangle, and the equation expressing the value of the 

 stability in that case, is 



(296) . 



which is manifestly the same expression as that which we obtained for 

 the triangle in the first variety, where the ordinates were supposed to 

 be parallel to the depth; hence, the value of the stability when 

 estimated in numbers will also be the same. 



502. Again, if we suppose the bounding curve of a cross section to 

 be the same as the common parabola, then 11=12, and this being sub- 

 stituted in the general equation, the expression for the stability in this 

 case, is 



(297) . 



the very same as for the triangle ; hence it appears, that when the 

 ordinates are parallel to the breadth, the stability for a triangular 

 section is the same as it is for a section in the form of the common or 

 Apollonian parabola. 



503. But when the boundary of the section is in the form of a 

 cubic parabola, then n =: 3, which being substituted in the general 

 equation, the expression for the value of the stability in this case, is 



s= * (*.!.>. .'.': r. (298) 



If this equation be compared with the corresponding one for the 

 cubic parabola, in the case when the ordinates are parallel to the 

 depth, it will be seen that the present form is superior in point of 

 stability, since it requires a less breadth in proportion to the depth to 

 offer an equal resistance. This inference is drawn from a comparison 



