[12] This experimental method, it may be explained, has long been practised in connection with ships built for the Royal Navy, and for a considerable number of years it has been systematically followed in some leading merchant shipyards. Messrs A. & J. Inglis, Pointhouse, Glasgow, and Messrs Wm. Denny & Bros., Dumbarton, were amongst the earliest firms to systematically adopt the practice. With the former it has been customary to incline every vessel of distinctive type built by them since 1871, and with the latter the practice has been constantly followed from a date somewhat subsequent. For some years past other firms on the Clyde and elsewhere have adopted the method, the data so accumulated being found an admirable basis from which to estimate the height of the centre of gravity in proposed vessels. Tables giving the results of inclining experiments made on various types of merchant steamships and sailing vessels will be found in “White’s Manual of Naval Architecture,” pages 82-87. [13] From the first volume (1860) of the Transactions of the Institution of Naval Architects, it is seen that Dr Inman, Samuel Read, and Dr Woolley had each already found different methods of simplifying Atwood’s calculations. [14] Various other methods of simplifying the calculations based on Atwood’s theorem were subsequently proposed, and one or two different methods also brought forward—notably one in 1876 by the late Mr Charles W. Merrifield, afterwards improved by the late Professor Rankine, and one by Mr J. Macfarlane Gray, of the Board of Trade, described by that gentleman in 1875, but since considerably improved. Most of them were laid before the Institution of Naval Architects in papers which will be found enumerated in the list at end of chapter. While such propositions did not contribute directly to bring the problem of stability to its presently accepted form, they deserve to be remembered as tokens of the great labour and skill which have been expended in founding and developing this branch of scientific naval architecture. [15] “On Cross-Curves of Stability; their Uses, and a Method of Constructing Them, Obviating the Necessity for the Usual Correction for the Differences of the Wedges of Immersion and Emersion.” [16] A detailed description of this valuable instrument will be found in Appendix. [17] Space forbids any detailed reference to these, but the names of the papers and their respective authors will be found enumerated in the list at end of chapter.