Stability with Draught of Water in Ships. 215 



upward pressure of the water act, either to restore the vessel to the 

 upright position or to produce farther inclination. The factors v, 

 V, and h-Ji z are readily calculated from the external dimensions and 

 form of the ship by means of Simpson's rules ; the position of the 

 point B, the centre of buoyancy in the upright position, is similarly 

 obtained ; and G is either determined by experiment, or by calculating 

 in detail the weights and statical moments of the component parts of 

 the structure and loading. Mr. P. K. Barnes, one of the present Chief 

 Constructors of the Navy, read a paper before the Institution of 

 Naval Architects, in 1860, in which he showed how the requisite 

 calculations could be made concisely and with facility. 



Notwithstanding Atwood's demonstration of the imperfect and 

 unreliable standard of stability furnished by mere metacentric height, 

 and his theorem for enabling the righting moments at large angles of 

 inclination to be determined, the step which it may now appear 

 would naturally follow was not actually taken till 1867. In that 

 year a question arose at the Admiralty respecting the stability 

 of some low freeboard monitors at very large angles of inclination ; 

 and Sir E. J. Reed, then Chief Constructor of the Navy, directed 

 the matter to be investigated. It was placed in the hands of Mr. 

 William John, who made the calculations, and embodied them in the 

 graphic form now known as the curve of stability. 



FIG. 9. 



Thus in fig. 9, if OX be an abscissa line, upon which the various 

 equal divisions represent angles of inclination of a ship, and any 

 ordinate, such as P, be the length of GZ (see fig. 8) at the angle of 

 inclination , OPX will be the curve of stability for the particular 

 draught of water and position of centre of gravity under considera- 

 tion. The results of Mr. John's calculations were described in a paper 

 read by Sir E. J. Reed before the Institution of Naval Architects in 

 1868; and a further paper containing an improved method of 

 applying Atwood's theorem to the calculation of stability upon this 

 extended scale, was read before the same Institution by Messrs. John 

 and White, in 1871. 



