400 OF THE STABILITY OF STEAM SHIPS. 



where > DC is the breadth of the vessel at the water line when 

 upright and quiescent, C?=LK the corresponding depth, FPC 

 the angle of inclination from the upright position, n the exponent 

 denoting the order of the parabolic section, and S the stability. 



489. If we examine the structure of the above equation, it will 



readily appear, that while b* is greater than - ' , the stability is 



n | A> 



positive, and the vessel endeavours to regain the upright position ; if 

 these two quantities are equal to one another there is no stability ; 

 and if the latter exceeds the former, the stability is negative, and the 

 vessel oversets. Hence it appears, that between the breadth and 

 depth of the vessel, a certain relation must obtain to render it fit and 

 sufficiently stable for the purposes of navigation; and it is further 

 manifest, that the stability increases directly as the exponent of the 

 ordinate, so does the area of the transverse section ; but in order to 

 give the proper degree of stability, the breadth must increase more 

 rapidly than the depth. 



By giving different values to the symbol n in the preceding 

 general equation, we shall obtain expressions to indicate the stability 

 for sections of different forms ; thus for instance, if n zz 1 the section 

 is a triangle, and the expression for the stability becomes 



(291). 



490. This equation is very simple, and can easily be illustrated by an 

 example ; the practical rule for its reduction may be expressed in the 

 following terms. 



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

 when the vessel is upright, subtract twice the square of the 

 corresponding depth ; multiply the remainder by the breadth 

 drawn into the natural sine of the angle of inclination, and 

 one twelfth of the product will express the stability. 



491. EXAMPLE. A floating body in the form of a triangular prism, 

 has its breadth at the water line equal to 28 feet, the corresponding 

 depth under the water equal to 19| feet, and its density equal to the 

 density of water; now, suppose the body to be in a state of equili- 

 brium when the axis is vertical ; what will be its stability, or what is 

 the relative value of the force by which it would endeavour to regain 

 the upright position, on the supposition that it has been deflected 

 from it through an angle of 15 degrees ? 



This is obviously a case that is not likely to occur in the practice 



