PRESIDENTIAL ADDRESS. 471 



T 5 T 9 

 the cases =- = • and =.- =>~ the results show baulked oscillations in which, while the 

 T, 9 T, 5 



vessel swings towards the vertical, she does not reach it hut swings hack again. The 

 lengthened value of T here also gave better results than for shortening it. 



The results given above are greater than would be obtained in practice, because 

 resistancehas been neglected. Later he determined the effect of resistance upon rolling 

 in still water free from waves. He determined the law of resistance and found it to 

 vary partly as the angular velocity and partly as the square of it. He rolled a ship, 

 and after she was allowed to roll free from disturbance he measured the angle of 

 inclination at the end of each roll. These showed the rate of extinction of the rolling 

 due to the resistance. The loss of extreme angle of roll between one roll and the 

 next represented the work done by the ship in rolling. It is possible to calculate 

 the work done in inclining the vessel to any angle, and the difference between the 

 amount of work thus done in two different angles represents the difference in work 

 necessary and therefore work done in resistance to bring the ship to these angles 

 of inclination. Hence the work done by resistance between two consecutive rolls 

 can be actually measured by measuring the extreme angle of inclination in successive 

 rolls. 



Having determined the resistance in terms of angles of roll and time, it was easy 

 to determine the law which represented the resistance in terms of the angular velocity. 



In applying this to waves, all that is necessary is to take account of the fact that 

 the position of equilibrium about which the ship oscillates is the normal to the effective 

 wave-slope. This normal has a definite oscillation about a fixed vertical. It is, 

 therefore, possible to determine the angle of inclination in terms of time. 



As these angles of roll may be considerable, the assumption upon which the general 

 solutions for unresisted rolling, already given, were based will not hold. The actual 

 moments of stability depend upon the form of the ship and the position of its centre 

 of gravity, and as these vary in different ships it is only possible to obtain the relation 

 between inclination and time by a special investigation in each case. A solution by 

 a method of graphic integration was devised by Mr. W. Froude and has been applied 

 to a very small number of cases. The information necessary to obtain a solution 

 in any one case is as follows : — 



(1) A curve of righting levers in terms of angle of inclination. This is called a 

 curve of statical stability. 



(2) The form and period of the wave on which the ship is supposed to be placed 

 broadside on. 



(3) The constants which determine the actual value of the resistance moment in 

 terms of the angular velocity. These can be obtained by rolling the ship in still 

 water and observing the rate of extinction of rolling when that extinction is due to 

 resistance only. The form of the curve of extinction can be obtained by rolling a 

 model of the ship, but the actual ordinates of the curve for an actual ship can only 

 be obtained by experiment on the ship herself, or by inference from a similar ship of 

 approximately the same size, form, and arrangements. 



A consideration of these three necessities for the solution of one particular case 

 shows that a considerable amount of work is necessary for determining the angle of 

 inclination in terms of time. In waves even this solution can only be made for one as- 

 sumed maximum angle of inclination as a starting condition. For instance, in any case 

 where a ship is assumed to start with a maximum inclination of 20° it is only possible 

 to obtain one solution of angles of inclination in terms of time. If we take another 

 maximum angle of inclination, another complete solution is necessary. The work of 

 each solution is considerable. 



For ships which vary much in draught and condition of loading it is evident that 

 for each ship the work of complete investigation for all the conditions of loading of 

 different waves and different angles of maximum inclination is very great. For this 

 reason the investigation of rolling by the Froude graphic method has only been made 

 for a very small number of cases, and our knowledge of the actual angles of inclination 

 of ships obtained by this method is very small. 



The curve of statical stability is worked out for many ships in a few conditions of 

 draught and position of centre of gravity. These curves are of little practical value, 

 because they only serve as comparisons between ships. It is assumed that if a ship 

 has a fair range of statical stability, i.e., that the angle of vanishing statical stability 



