955 



mical stability. It is a second object of the paper to determine the 

 conditions of quick and sloiu rolling. 



The remarkable disparities observed between different vessels in 

 respect to rolling in the recent experimental squadrons give great 

 interest to this inquiry. It is moreover of much practical import- 

 ance on account of the detriment to which ships are liable by reason 

 of their wear and tear from quick rolling, and its interference with 

 their qualities as ships of ivar. 



When a ship heels over its centre of gravity is vertically displaced, 

 and also the centre of gravity of the water it displaces (technically 

 called its immersion) ; and the author, in the first place, shows that 

 the difference of these vertical displacements, with reference to a 

 given inclination, multiplied by the Aveight of the ship, is a measure 

 of its dynamical stability ; so that if there be any number of ships, 

 and a common inclination (say 20°) be assumed for all, if this 

 difference be calculated in respect to each ship, and multiplied 

 by the weight of the ship, then that in respect to which this product 

 is the greatest would be dynamically the most stable ship, or would 

 heel the least, if all were subjected to the same force of the wind or 

 the waves under the same circumstances. Stated/?«% and under its 

 most general form, this theorem is as follows : — 



" The work^^ which must be done upon a ship to cause it to heel 

 through a given angle, is equal to that necessary to raise it bodily 

 through a vertical height equal to the difference of the vertical dis- 

 placements (when thus heeling) of its centre of gravity and that of 

 the water it displaces." 



The Lords Commissioners of the Admiralty having directed that 

 this theorem should be subjected to the test of experiment, experi- 

 ments were undertaken for that object by Mr. Fincham, Master Ship- 

 wright of Her Majesty's Dockyard, Portsmouth, and by Mr. Rawson, 

 the particulars of which are given in this paper. 



It was necessary for this verification to do a given amount of work 

 upon a floating body, causing it to incline through a given angle, 

 and then to ascertain whether, as the theorem states, this amount of 

 work was that necessary to raise the vessel bodily through a height 

 equal to the difference of the vertical displacements of its centre of 

 gravity, and that of its immersion whilst in the act of so inclining. 

 For this purpose a model vessel was floated in a tank, and being 

 fitted with a mast and long yard, a weight was attached to one ex- 

 tremity of this yard, and the vessel allowed to heel over under the 

 influence of this weight. The extreme inclination to which it heeled 

 was then accural ely ascertained by an ingenious method devised by 

 Mr. Rawson, and the vertical descent of the deflecting weight mea- 

 sured. The product of this descent by the deflecting weight gave 

 the icork done upon the body to incline it from its position of equili- 

 briu7n, and by the theorem this should be equal to the weight of the 

 vessel, multiplied by the difference of the two vertical displacements 

 spoken of above. The forms of the vessels experimented on were 

 so selected that the positions of the centres of gravity of their im- 

 * Measured in lbs. raised one foot. 



