Withy. — On the Stability of Ships. 667 



expenditure may be measured by calculating the height 

 through which the vessel has been lifted and multiplying it 

 by her weight. The operation is rendered simple by the 

 knowledge of the fact that a ship's weight corresponds to that 

 of the water which she displaces. In listing to a given angle, 

 we have seen, under our assumption that a mere section 

 represents the solid, that the area of the section is increased 

 on the lee side and reduced to windward by the area of the 

 respective triangles of immersion and emersion. We have 

 further seen that, while these triangles are equal in area, they 

 are, in all but circular sections, dissimilar in form, and have 

 therefore different horizontal moments. In all cases, there- 

 fore, where the moment of immersion is greater than that of 

 emersion, the centre of buoyancy is moved to leeward. The 

 additional fact to which I now wish to ask your attention is that 

 these triangles have different vertical moments, and that they 

 consequently raise the centre of buoyancy vertically. Having 

 ascertained by measurement of the triangles what this vertical 

 rise amounts to, we have simply to multiply it by the area of 

 one of them to obtain a comparative measure of the work done 

 in the act of careening. It may also be found by multiplying 

 the rise of the centre of buoyancy by the total area of the 

 inclined midship section. This measure, when solid is sub- 

 stituted for area, is known as the dynamical stability at the 

 given angle of heel. 



The different nature of these two measures may be illus- 

 trated by a reference to fig. 3, Plate LI., which represents a 

 cylindrical model when rolled up an inclined plane. The stati- 

 cal energy of the body in either of the two right-hand positions 

 is measured by its weight multiplied into the length of the 

 respective righting-levers, or the distance in each case from its 

 point of contact to the perpendicular from the centre of gravity. 

 The dynamical work done in raising it to these positions is 

 measured by its weight multiplied into the i-espective vertical 

 distances through which its centre of gravity has been raised. 

 This latter measure is different from the condition of balancing. 

 It consists of an amount of work done upon, and stored up in, 

 the body which will be given out again during its return to 

 the upright position. In the case of a ship we can imagine 

 her lying at a wharf, and that the inclination was produced 

 by hooking a crane-chain to her rail and heaving av^'ay at the 

 handles. 'When she had been careened, if the handles were 

 let go, they would be made to fly round by her return to the 

 upright position. A clock-weight, after being wound up, does 

 just the same thing, and in running down makes the clock go 

 by giving out again the work stored up in it. 



It v/ill scarcely be necessary to remind you that stability 

 is a measure which varies with every change in the stowage 



