Withy. — Ow the Stability of Sliips. 663 



lation for it stops short at an early stage of the more com- 

 pHcatecl one required to ascertain the range of stability. 



We may now pass from initial stability to consider what 

 the range of stability is. It is not only of importance that we 

 should know that a vessel can present a fair amount of initial 

 resistance to an inclining force, but that she can increase and 

 maintain it up to large angles. It will be here necessary 

 to explain what the righting-lever is. It has been shown 

 that when a vessel is at rest her weight is pressing down 

 through its centre and the buoyancy up through its centre in 

 the same vertical line. Hence a condition of equilibrium 

 exists. Two equal forces arc acting upon a given point in 

 opposite directions. But let some power be applied to careen 

 her — say the usual one of the wind blowing sideways on her 

 sails. This will destroy the first condition of equilibrium, and 

 a struggle will take place for a time between the wind and the 

 vessel's stability. She will yield easily at first, but, at some 

 particular angle, will have acquired such an access of stability 

 that the wind can press her no further. Thus another con- 

 dition of equilibrium is produced. The wind and the stability 

 have both met with their match. Can we ascertain the force 

 which each is exerting? Yes; by first ascertaining the length 

 of the righting-lever which she possesses at the given angle of 

 heel. 



We must proceed by calculating the centre of buoyancy in 

 the inclined position, and then draw a perpendicular line 

 upwards from it. Then we must find, by the experiment to 

 be explained presently, the position of the centre of gravity of 

 the ship, and draw a line perpendicularly downwards from it. 

 The horizontal distance between these two lines, representing 

 the direction of forces, may be considered as a lever or couple. 

 This is known as the righting-lever. Now, the weight and 

 buoyancy are known to be equal. Therefore, if we multiply 

 either of them — say the buoyancy — in tons by the length of 

 the lever in decimals of a foot we shall get an expression of 

 foot-tons as the actu.al measure of stability. The force of 

 the wind has been shown to be exactly equivalent to this 

 resisting-power, or stability of the vessel, seeing that it suc- 

 ceeded in forcing her to, and keeping her at, a certain angle of 

 inclination. 



It will be seen now that, while the metacentric height is 

 not the actual multiplier for obtaining the measure of stability, 

 yet, if its relation to the length of righting-lever is constant 

 in all vessels at equal angles of heel, it must be very valuable 

 as a comparative measure of stability as between them. Their 

 relationship may be further explained, and the promised proof 

 given, thus : If at a given angle the centre of buoyancy appears 

 further to leeward than at some lesser angle it is evident that 



