OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 377 



in magnitude to the displacement, will likewise be equal to the whole 

 weight of the vessel. 



The quantity is necessarily given from the circumstances of the 

 case, and may be of any magnitude whatever, and therefore, the 

 only quantities required to be ascertained, for the purpose of dis- 

 covering the momentum of the ship's stability, are v and d in the 

 numerator of the fractional term, the one denoting the magnitude of 

 the volume which becomes immersed in consequence of the inclina- 

 tion, and the other, the distance through which the centre of gravity 

 of that volume is moved in a horizontal direction, during the deflexion 

 of the ship from the upright and quiescent position. In order, there- 

 fore, to facilitate the determination of those quantities, the following 

 observations are necessary. 



467. If a straight line be conceived to pass through the centre of 

 gravity of the ship, in the direction of its length and parallel to the 

 horizon, traversing from the head to the stern of the vessel ; then, such 

 a line is called the longer axis of the vessel ; it is the same with the 

 axis of motion described in the fifth definition preceding, and is so 

 called, for the purpose of distinguishing it from another line also hori- 

 zontal, which passes through the centre of gravity at right angles to 

 the former, and is called the shorter or transverse axis of the vessel ; 

 it is on this axis that the vessel turns in the process of pitching, a 

 motion which is easily understood by considering an alternate eleva- 

 tion and depression of the head and stern. 



468. A vertical plane drawn through the longer axis, when the 

 vessel floats in an upright and quiescent position, divides it into two 

 parts which are perfectly similar and equal to one another, and in this 

 respect at least, the figures of vessels may be considered regular, 

 although that their forms are not otherwise restrained to any uniform 

 or particular proportions. 



From the similarity and equality of these two divisions, it necessa- 

 rily follows, that when a vessel floats in a state of upright quiescence, 

 the similar parts on the opposite sides of the plane of division will 

 be equally elevated above the water's surface. A ship thus floating 

 in a position of equilibrium, may be conceived to be divided into two 

 parts by the horizontal plane which is coincident with the water's 

 surface, and the section formed by this plane passing through the 

 body of the vessel, is called the principal section of the water ; it 

 corresponds with the plane of floatation in the particular case where 

 the vessel is upright and quiescent, as will readily be perceived by a 

 reference to the ninth definition preceding. 



