OF THE STABILITY OF STEAM SHIPS. 405 



of the constants belonging to the negative term, for in the one case 

 it is double of what it is in the other, and consequently, in the latter 

 case, a less breadth is necessary to give a positive result. 



504. Lastly, if n zr 5, then the parabola which bounds the trans- 

 verse section A KB of the vessel, is defined by the equation px=iy s , 

 as in the annexed figure, in 

 which the several letters indi- 

 cate the parts already men- 

 tioned, viz. DC the breadth, 

 LK the depth of the vessel, 

 E F the water line, k' k the line 

 of support, y the ordinate 

 parallel to the breadth, x the 

 abscissa ; then, the expression 

 for the stability in this case, becomes 



.,/ (299 , 



from which it appears, that the higher the order of the parabola, the 

 less increase of breadth is necessary with the same depth to obtain 

 an equal degree of resistance ; but in the case when the ordinates are 

 parallel to the depth, as in the first variety, the contrary takes place, 

 a greater increase of breadth being necessary for the same purpose. 

 Hence we conclude, that the higher the order of the parabola, the 

 greater is the degree of stability ; but the form in which the ordinates 

 are parallel to the breadth, is preferable to that in which they are 

 parallel to the depth; and, as Mr. Tredgold justly remarks, " this 

 species of figure may be easily traced through all the varieties of 

 form, and it has obviously a decided advantage in point of stability, 

 and it is so easy to compute its capacity and describe it by ordinates, 

 that it is much to be preferred to the elliptical figures which foreign 

 writers have chosen for calculation." 



505. In order that the stability may be the same at every section 

 throughout the whole length of the vessel, this being a necessary 

 condition in the most advantageous cases, the breadth should be 

 every where in the same ratio to the depth ; for when this is the case, 

 the vessel will suffer no lateral strain from a change of position. 

 The preceding determinations relate to the vessel's stability when the 

 inclination is made about the longer axis ; but the position of the 

 shorter axis, round which the ship revolves in pitching, in all cases of 

 practical inquiry, must also be considered ; but since the investigation 

 sf the several conditions would be similar to that which refers to the 

 longer axis, we deem it unnecessary to extend the inquiry any further. 



