436 



Variation in Stability in Ships. 



[Mar. 13, 



follows 'that, in such elementary forms of floating bodies, lightness of 

 draught has the same effect upon stability as lowness of freeboard; 

 and if a low freeboard is unfavourable to stability, so also, and 

 precisely to the same extent, is a correspondingly light draught of 

 water. This proposition can be made still more general, as it applies 

 to homogeneous bodies of any form of cross-section which revolve 

 about an horizontal axis fixed only in direction. From this may be 

 deduced the results given by Atwood in his papers read before the 

 Royal Society in 1796 and 1798 respecting the positions of equilibrium 

 and other peculiarities connected with the stability of floating bodies. 



In considering the stability of a ship at various draughts of water, 

 and comparing it with that of the class of figures above described, 

 modifications require to be made for the departure from symmetry of 

 form, and for the extent to which the vertical position of the centre 

 of gravity differs from what it wo aid be if the external surface 

 enclosed a homogeneous volume. This has been attempted in the 

 present paper, and curves of stability, which I call cross curves, have 

 been given for various geometrical forms of floating bodies, and also 

 for a large passenger steamer of ordinary type, showing how the 

 stability varies with draught of water at constant angles of inclina- 

 tion. In dealing with these cross curves of stability the curves of 

 righting moments require to be constructed, and not merely curves of 

 lengths of righting arm. The ordinary curve of stability is usually 

 made for lengths of righting arm, because the displacement is con- 

 stant, and the same curve therefore gives upon different scales, either 

 lengths of righting arm or righting moments. In the cross curves of 

 stability, however, such as are now being dealt with, draught, and 

 therefore displacement, is one of the variable quantities, and carves 

 of righting moments are of a very different character from curves of 

 righting arm. The curves given in the figures are therefore, in all 

 cases, curves of righting moments. Complete cross curves for a ship, 

 from which ordinary curves of stability can immediately be obtained 

 for any draught of water and position of centre of gravity, can be 

 constructed in a few days with the aid of Amsler's mechanical 

 integrator. 



The main object of this paper is to show the necessity of regarding 

 the stability of a ship from the point of view of variation of righting 

 moment with draught of water, the angle of inclination being 

 constant, instead of from that of variation of righting moment with 

 angle of inclination, the draught being constant, as is usually done ; or 

 rather of considering the subject from both points of view instead of 

 almost exclusively from the latter. It also shows that it is necessary 

 to investigate more fully than has formerly been done, the moments 

 and range of stability of ships and other structures that may be 

 intended to float at very light draughts of water. 



