376 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



3. PRINCIPLES OF THE STABILITY OF SHIPS. 



465. We have seen from the formula (282), that the measure of 

 stability, when the body is inclined through any angle from the per- 

 pendicular, is 



a'd 



in which equation, the symbol x expresses the horizontal distance 

 between the two vertical lines, one of which passes through the centre 

 of effort, and the other through the centre of buoyancy. 



The same principle has now to be applied in estimating the stability 

 of ships, and this object will be attained, if either by calculation or 

 geometrical construction, we find the value of rr, which in the inclined 

 position of the diagram to Problem LXI. is represented by GS or rz ; 

 then, if we suppose the whole weight of the ship or floating mass to 

 be denoted by w, it is manifest, that the momentum of stability will 

 be expressed by the weight of the vessel drawn into the horizontal 

 distance between the vertical lines above described ; that is, 



771 WXj 



where 772 denotes the momentum of stability, or the effort by which 

 the vessel endeavours to regain the upright position, from which it is 

 deflected by the action of the wind, or some other equivalent force 

 similarly applied. 



If, therefore, we put v to denote the whole volume of fluid displaced 

 by the immersed part of the vessel, and v for the volume which is 

 depressed below the plane of floatation, in consequence of the vessel 

 heeling from the upright position through an angle equal to0; then, 

 the general form of the equation for the momentum of stability becomes 



dv > 



- aSm '^ W; - (282-). 



466. Now, in applying this expression to any particular case in 

 practice, it is understood, that the position of the centre of gravity of 

 the entire ship, and also the position of the centre of gravity of the 

 immersed volume when the ship is upright and quiescent, are both 

 known, and consequently, the distance between those centres, which 

 is represented by the line Gg or GW, is a given or assignable quan- 

 tity ; and moreover, the total displacement occasioned by the floating 

 body, is supposed to have been determined by previous admeasure- 

 ments, and hence, the weight of a quantity of water, which is equal 



