36 REPORT— 1869. 



analogous to that of a raft ; while the condition of the keel, the sharp part 

 of the floor, and the gripe and dead wood (or fine parts of the ends) is analo- 

 gous to that of the hoard floating edgewise, so that the ship is iinder the 

 action of two conflicting sets of forces — gravity, centrifugal force, and 

 pressure (constituting what id ay he called stiffness), tending to make her 

 roll with the waves, like the raft ; and tlie action of the water on the keel 

 and sharp parts of the hull, which may be called Jceel-resistaiice, tending to 

 make her roll against the waves, like the hoard, and hence that she will take 

 some kind of intermediate motion. 



It has been pointed out, however, by Mr. Proude and Professor Eankine * 

 that there is an essential distinction between the two sets of forces before 

 mentioned, in consequence of which, though conflicting, they are not directly 

 o]3posod — namely, that the stiftness is an active force, which tends not only 

 to prevent the ship from deviating from a position upright to the effective 

 wave-surface, but to restore her to that position after she has left it, with a force 

 increasing with the deviation ; while the keel-resistance is merely a passive 

 force, opposing the deviation of the ship from the position of the originally 

 vertical columns of water, with a force depending, not on that deviation, but 

 on the velocity of the relative motion of the ship aiul the particles of water, 

 and not tending to restore the ship to any defluite position. Hence those 

 two kinds of force cannot directly counteract, but only modify one another. 



For the mathematical investigation of the action of those forces reference 

 must be made to the original papers in the ' Transactions of the Institution 

 of Naval Architects.' The following ai-e the general conclusions : — 



The permanent rolling of a ship of very great stabihty, and without any 

 sensible keel-resistance, is governed by the motion of the effective wave- 

 surface, so that she rolls vitJi the luaves or Kke a raft. 



"When the period of unresisted roUing of the vessel is to the wave-period 

 as a/2 : 1, the permanent rolling is wholly governed by the motion of the 

 originally vertical columns of water ; so that she rolls against the ivaves, like 

 a board of no stability floating edgewise. 



In both of the preceding cases the vessel is upright when the trough or 

 crest of a wave passes her, and her angle of heel is equal to the steepest slope 

 of the eflective wave-surface. 



When the period of unresisted roUing of the vessel is less than the above 

 value, her upright positions occur hefore the arrival of the troughs and crests 

 of the waves, and her angle of heel is greater than the steepest slope of the 

 effective wave-surface. 



The greatest angle of heel in permanent rolling occurs when the period of 

 unresisted rolling of the ship is equal to that of the waves, and it exceeds the 

 slope of the waves in a proportion which is " the greater the less the keel- 

 resistance, and becomes infinite when the keel-resistance vanishes. Thus 

 isochronism with the waves is the worst quality that a ship can have as 

 regards steadiness and safety. 



When the period of unresisted rolling of the vessel exceeds that of the 

 waves in a greater ratio than that of /^2 : 1, her upright positions occur 

 after the arrival of the troughs and crests of the waves, and her angle of 

 heel is less than the steepest slope of the waves. 



The forced or passive oscillations of ships arc those which produce the 

 most severe strains, because of their continual recurrence, the free oscilla- 

 tions being gradually extinguished by the resistance of the water. It 



* Trans. I. N. A. for 18G3-G4, 



