To complete the representation of stability as it should be known for merchant ships, it is now recognised that curves showing the stability at every possible draught of water and for different positions of centre of gravity should be constructed. By means of “cross-curves” of stability, or curves representing the variation of righting moment, with draught of water at fixed angles of inclination, this comprehensive want can be met with something like the necessary expedition. From such curves it is a simple operation, involving no calculation save measurement, to construct curves of the ordinary description, showing the righting moment at all angles for any fixed draught of water and position of centre of gravity. Professor Elgar was the first to publicly direct attention to this valuable development of stability investigation of merchant ships, doing so in an able paper “On the Variation of Stability with Draught of Water in Ships,” read before the Royal Society on March 13th of the present year. Simultaneously with Prof. Elgar’s employment of such curves in actual practice their use had been independently instituted by Mr William Denny in his firm’s drawing office, and the mode in which they were worked out in this case was communicated in a paper read by Mr Denny in April of the present year before the Institution of Naval Architects.[15] Several important improvements with respect to simplifying and shortening calculation distinguish the method employed by Mr Denny, and that gentleman, in the paper referred to, accords individual credit to members of the scientific staff in his firm’s employ, who, on being entrusted with the work of calculation, brought considerable originality to bear upon their labours. The cross-curves described by Prof. Elgar were constructed from a series of curves of stability calculated in the ordinary way. This, however (as pointed out in an after-note to that gentleman’s Royal Society paper), is less simple and very much less expeditious than the method carried out under Mr Denny, which consists in calculating the cross-curves directly by applying Amsler’s mechanical integrator[16] to the under-water portion of the ship instead of to the wedges of immersion and emersion, thus determining at once the positions of the vertical lines through the centres of buoyancy at the required angles of inclination. As thus carried out a complete set of cross-curves can be produced with about one-third the labour involved in employing the older method. The ease and rapidity with which ordinary curves for separate draughts can be taken from cross-curves has already been commented upon.