Unless the plan of lines of a similar vessel of nearly the same dimensions is at hand, the design of a new vessel is in many instances done without previous calculation being made to ensure at once obtaining the desired displacement. Special methods of quickly arriving at this result are, however, not uncommon in mercantile shipyards, and generally speaking the chief draughtsmen in the employ of large firms doing a varied class of work have rules derived from long experience, though not perhaps definitely systematised, by which they are guided.[10] Irrespective of all such special methods, however, the work of designing is now greatly shortened and simplified by means of Amsler’s “planimeter,” an ingenious instrument for measuring areas now becoming well known.[11] By employing the instrument in question, the draughtsman need not too laboriously strive after the exact displacement at first, as the time occupied in ascertaining what displacement any set of lines gives, and in the consequent fining or filling out, is very considerably less than by the ordinary methods. * * * * * The question of stability, which has next to be considered, is one of great difficulty and intricacy, and it was not till the middle of last century that some of the principles upon which it depends began to be understood. Bouguer showed in 1746 that the position of the “metacentre” limits the height to which the centre of gravity of a floating body may be raised without making it unstable, and that the righting moments at small angles of inclination from a position of stable equilibrium are proportional to the height of the metacentre above the centre of gravity. As the position of the metacentre for any given draught of water is easily determinable when once the volume of displacement and the centre of buoyancy at that draught have been ascertained, it has been the practice for a very long time to construct a curve representing the height of the metacentre at all draughts, and to use it for showing the limits above which the centre of gravity cannot be raised with due regard to the stability required for the practical working of vessels and for purposes of safety: By the method of “inclining” vessels, already described (see outline of fundamental principles, page 98), the determination of the precise position of the centre of gravity is rendered comparatively simple.[12]