20 



Prof. F. Elgar. On the 



[Jan. 14, 



r© r© 



XM hi fig. 2 represents d\ cjxdO—o\ GadO, or the energy expended 

 Jo Jo 



in inclining an unit of length at X against the resistance of the righting 

 moment to the angle G. If similar values be determined for units of 

 length at each of the other ordinates, and a curve MMM be drawn 

 through the points so obtained, MMM will give the longitudinal dis- 

 tribution of the work done against the resistance of the righting 

 moments, or of what was called by Canon Moseley the dynamical 

 stability. 



Let EEE in fig. 2 be a curve which shows in a similar manner the 

 longitudinal distribution of the energy of rotation. XE will be the 



2 



value of — wlc 2 for the unit of length at that ordinate : and the other 

 2g 



ordinates of the curve will be the values of — ivk 2 at the correspond- 



2 ? 



ing points in the ship's length. 



The difference between the energy of rotation of any portion of the 

 vessel's length AX and the work expended in inclining that portion, 

 in opposition to the moments of the forces exerted by its weight and 

 the fluid pressures upon it, is equal to the area ME A in fig. 2. This 

 area measures the excess of energy of rotation in the volume between 

 A and X, which is communicated through the hull of the ship to some 

 other part of her length at which the energy of rotation per unit of 

 length is less than the work required per unit of length to incline it to 

 the angle 6. This excess of energy is transmitted, by means of a 

 twisting moment upon the hull, to the part of the ship's length where 

 it is utilised in overcoming resistance. 



A graphical representation of the longitudinal distribution of the 

 mean twisting moments which act upon the hull when the vessel is 

 rolling to an angle on each side of the upright position, may be 

 made by means of a curve so that any ordinate of the curve will give 

 the mean value of the twisting moment upon a , section at the point for 

 which the ordinate is drawn. 



The values thus obtained for the twisting moments will be mean 

 values only. The variation of twisting moment at any section of the 

 hull during a roll, and consequently the maximum twisting moment, 



