26 REPORT— 1869. 



incidentally to the design of these and to the apportionment of engine- 

 power and driving-speed. 



Such experiments are quite heyond the means of any body but the Govern- 

 ment of a naval power in time of peace, possessing ships which must be 

 exercised with their crews and staff of officers. There would of course be 

 extra expense attending such trials ; but this expense is in no way commensu- 

 rate with that of building experimental vessels, or arriving tentatively at 

 the suitable forms and positions for propellers. 



We therefore recommend that the Council of the British Association 

 should authorize a deputation to apply to the Admiralty to provide for such 

 a set of experiments in the course of the summer of 1870 ; also, that the 

 Council should appoint a Committee, consisting of three Members of the 

 Association, to confer mth officers of the Admiralty respecting the detail of 

 the experiments, and that the Admu'alty should be requested to give an 

 opportunity to the Members of that Committee of taking a share in the 

 observations, in order that they may be enabled to make an independent 

 report upon the results. 



EOLLING OF SHIPS. 

 Stability and Free Oscillation. 



The statical stability of a ship in still water depends upon two equations 

 and an inequality. 



Its weight must equal that of the fluid it displaces, or it will adjust itself 

 by changing its water-line. This involves a first equation. 



The centre of gravity of the displaced water must be in the same vertical 

 line with the centre of weights, or there will be a couple which will produce 

 rotation ; after which the ship will take up a fresh position. This involves 

 a second equation. 



In case of a small angular displacement, the centre of gravity of the 

 displaced water (or cextre of BroTAXcv) must move out faster than the 

 centre of weights ; otherwise, on the slightest derangement, there will be 

 an upsetting couple, that is to say, the equilibrium is unstable. This in- 

 volves an inequality. 



The arm of the couple is the horizontal distance between the centres of 

 weight and buoyancy. The moment of the couple is the product of this 

 into the weight, or, what is the same thing, the displacement of the ship. 

 If the centre of buoyancj' moves out faster than the centre of weight as the 

 ship heels, there is a righting couple ; if not, there is an upsetting couple, 

 which tends to bring the ship to some new position of equilibrium. 



If we consider a vessel having a plane of sjTumetry like that in which 

 the masts, stern, stern-post, and keel of ordinary ships lie, and rolling trans- 

 versety, we gain much in geometrical simplicitj% and also in simplicity of 

 language. We arc enabled to deal with the mechanical questions by means 

 of plane geometry, and we are stOl able to extend them, when necessary, by 

 the ordinary rules of the composition of motion. For this purpose we have 

 only to consider the axis of motion as parallel to the plane of sj-mmetry and 

 to the water-section. The starical stability, as already remarked, is measured 

 by the weight, and by the horizontal distance between the centres of weight 

 and buoyancy. But when these coincide in horizontal position, as they do 

 when there is equilibrium, we are driven to some other measure in order to 

 avoid indeterminateness at the limit. For this purpose we avail ourselves 

 of the point at which the vertical line through the centre of buoyancy strikes 



