OF THE STABILITY OF STEAM SHIPS. 



403 



12 v - ;= 38x0.02157x75.1 n: 6 1.6 nearly. 



498. In order to pursue the inquiry a step further, let us suppose 

 that 7zz=5; then, by substituting this value of n in the general 

 equation for the value of the stability, we shall get 



(294). 



an equation which differs in nothing from those that precede it, but in 

 the value of the constant co-efficient of the negative term within the 

 parenthesis, a quantity which indicates the increase of breadth at the 

 water line, necessary to give the vessel the same degree of stability, 

 under the same depth and deflexion, which it possesses when bounded 

 by curves of the lower orders. 



499. If the curves which we have just considered were delineated 

 from a fixed scale, according to the relation that subsists between the 

 ordinates and the corresponding abscissas, it would be seen, that the 

 breadths towards the vertex become greater and greater as the exponent 

 of the ordinate increases; the figure therefore approaches continually 

 to the form of a rectangular parallelogram, and essentially coincides 



fc' 



with it, when the value of n 

 becomes infinite, as in the 

 parabola A KB, wherein DC is 

 the breadth, and LK the depth 

 of the vessel ; E F the water 

 line, and k'k the line of sup- 

 port in the inclined position ; 

 y the ordinate parallel to the 

 depth, and x the abscissa; 

 DPE the immersed triangle, I 

 and F PC the extant triangle. This extreme case has a manifest rela- 

 tion to the subject of stability ; for whatever may be the effect of 

 giving to the sides of vessels the forms of the higher orders of 

 parabolas, it is evident, that as the exponent of the ordinate is 

 increased, the stability will approach to that which would obtain if 

 the sides were made parallel to the plane of the masts. 



Now, it may easily be shown, that when the sides of the vessel are 

 made to coincide with the form of a conic parabola, (fig. art. 492,) 

 the stability is the same as when the sides are parallel planes ; hence 

 it is inferred, that if the sides of a vessel be formed to coincide with 

 a parabola of the lowest order, and another to coincide with one of 

 the highest, all other circumstances being the same, the stabilities 

 will be equal in these two cases. 



2 D 2 



