Stability with Draught of Water in Ships. 219 



or lengths of GZ, can be obtained by setting off a curve of sines as 

 in fig. 10 to radius BGr, and deducting the ordinates of this curve 

 from the corresponding ones of the curve of BB. This mode of con- 

 structing curves of stability has been rendered necessary by the great 

 variations in draught of water and position of centre of gravity that 

 have to be dealt with in many mercantile steamers. The demand 

 that has thus arisen for constructing cross-curves of stability, 

 i.e., curves showing the variation of righting moment with draught 

 of water at constant angles of inclination, has recently led to greatly 

 improved and more rapid methods of calculation being devised. 

 Amsler's mechanical integrator has been invaluable in bringing about 

 this desirable result, and it is now possible to make a complete set 

 of cross-curves of stability for a ship in a few days.* 



In considering the stability of a ship from the point of view of 

 variation of righting moment with draught of water, the angle of 

 inclination being constant, instead of from that of variation of 

 righting moment with angle of inclination, the draught being 

 constant, as was formerly done ; or, rather, in considering the 

 subject from both points of view instead of almost exclusively from 

 the latter, several interesting and important results are obtained, 

 which do not appear to have received the attention they deserve. 



It has already been stated that one of the first lessons taught by 

 the introduction of curves of stability was the decrease in the righting 

 moments at large angles of inclination, and the rapidity with which 

 stability frequently vanishes altogether, in vessels of low freeboard. 

 These are matters of great practical importance, and have attracted a 

 great deal of attention, on account of the numerous vessels of various 

 types which are more or less affected by them. The connexion be- 

 tween low freeboard and range of stability, and the manner in which 

 the" latter is affected by metacentric height and the position of the 

 centre of gravity, has latterly been well discussed and explained ; 



* The method thus described of calculating a series of ordinary curves of 

 stability and afterwards constructing cross-curves from them is tedious and compli- 

 cated. It is simpler and very much more expeditious to calculate the cross-curves 

 directly by applying the integrator to the under- water part of the ship, instead of to 

 the wedges of immersion and emersion ; and thus determining at once the positions of 

 the vertical lines through the centres of buoyancy at the required angles of inclina- 

 tion. By this means the necessity is avoided of calculating separately the volumes 

 of the wedges of immersion and emersion, and of correcting the positions first assumed 

 for the inclined water-lines in order to make these wedges approximately equal. 

 Mr. William Denny, of Dumbarton, was the first to call my attention to this very 

 important and useful simplification ; and it was described by him in a paper read 

 before the Institution of Naval Architects in April last. Other investigators have 

 also been working in the same direction, and several papers dealing with the exten- 

 sion and simplification of stability calculations will be found in the " Transactions of 

 the Institution of Naval Architects " for 1884, including one of great interest and 

 value by M. Daymard. 25th July, 1884. 



