While the vertical distance between the centre of gravity and the metacentre—commonly termed the “metacentric height”—forms a measure of the “initial stability,” or the stability at very small angles of inclination, it is imperfect by itself, and may be very misleading as regards the stability at larger angles. This was conclusively demonstrated by Atwood in his papers read before the Royal Society in 1796 and 1798, while other grounds for discrediting the standard of stability furnished by mere metacentric height were discovered subsequently, and have been signally emphasised, with additional reasons, by recent occurrences. Atwood, in the papers referred to, laid down a general theorem for determining the righting moments at any required angles of inclination possessed by a ship having a given draught of water and a fixed height of centre of gravity, the principle of which involved the use of the moments of the volumes of the “Wedges,” _i.e._, those parts of a vessel (see =W O W_{1}=, =L_{1} O L=, fig. 15), which become immersed and emerged as she is inclined. Several methods of simplifying Atwood’s calculations had been devised previous to 1861,[13] but in that year Mr F. K. Barnes, in a paper read before the Institution of Naval Architects, described a method of accomplishing this which until within recent years has been the one ordinarily adopted in computing the stability of a vessel at various angles of inclination.[14] Owing to questions having arisen at the Admiralty in 1867 respecting the stability of some low freeboard monitors at very large angles of inclination, Sir E. J. Reed, then Chief Constructor, directed the matter to be investigated. The work was placed in the hands of Mr William John, who embodied for the first time the results of the calculations in the form of a curve of stability, which exhibited the variations of righting moments with angles of inclination up to the particular angle at which stability vanished. The entire range of a vessel’s stability was thus made evident, and in such a form as enabled the general problem to be far more comprehensively and accurately treated than before. The results of Mr John’s labours 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 W. H. White in 1871. The loss of H.M.S. _Captain_, in 1870, as already pointed out near the beginning of this chapter, occasioned an immediate and serious regard for the stability of war vessels. This disaster, with other losses at sea from instability, also forcibly directed the attention of mercantile naval architects to the subject, and investigations on the same complete scale as those undertaken in the Admiralty have for some years been adopted in a few leading mercantile shipyards.