34 REPORT — 1869. 



and direction of motion relatively both to wind and waves, is far too com- 

 plicated even for statement in an exact mathematical form. 



If a ship floating passively in the water, and without any progressive 

 motion, were wholly without stability, her centre of gravity, centre of buoy- 

 ancy, and metacentre coinciding in one point, the motion assumed by that 

 point would be exactly that of the centre of gravity of the mass of water 

 displaced by the ship— that is to say, it would revolve once_ in each wave- 

 period in a vertical circle of the same diameter, with the orbits of the par- 

 ticles of water situated in the same layer. 



This motion of the ship has received the name of passive heavhig, that 

 term being understood to comprehend the swaying from side to side, as well 

 as the rising and sinking, of which the orbital motion is compounded. 



Half the difference between the extent of heaving of the ship and the 

 height of the waves is the extent to which, during the passage of the waves, 

 her depth of immersion amidships is liable to be alternately increased above 

 and diminished below her deptli of immersion in smooth water. It appears 

 that deep immersion and large horizontal dimensions, but especially deep im- 

 mersion, tend to diminish the extent of the heaving motion of the ship as 

 compared with that of the waves, and that the effect of those causes in pro- 

 ducing this diminution is greatest among comparatively short waves. 



The weight of the ship, being combined with the centrifugal force due to 

 her heaving motion, gives a resultant reaction through her centre of gravity 

 inchned to the vertical in a dii-cction which, for passive heaving, is perpen- 

 dicular to the wave-surface traversing the ship's centre of buoyancy (a sur- 

 face which may be called the effective ivave-surface) ; and that direction is 

 the apparent direction of gravity on board the ship, as indicated by plumb- 

 lines, pendulums, suspended barometers and lamps, spirit-levels, and the 

 positions assumed by persons walking or standing on deck. The equal and 

 opposite resulting pressure of the water, acting through the centre of buoyancy, 

 is in like manner compounded of actions due to weight and centrifugal force ; 

 and it acts in a line normal to the efi^ectivc wave-surface, that is to say, 

 parallel to the resultant reaction of the ship. Those tAvo forces balance each 

 other, not when the ship's upright axis is vertical, but when it is normal to 

 the effective wave-surface ; and when she deviates from that position, they 

 form a righting couple tending to restore her to it. Thus the stability of a 

 ship among wa\'es, instead of tending to keep her steady, as in smooth water, 

 tends to keep her upright to the effective wave-sia-face ; and such is the motion 

 of any vessel or other floating body having great stability and small inertia, 

 such as a light raft. This may be called passive roUinrj, or rolling luith the 

 waves. 



Passive rolling is modified by the inertia of the ship, which makes her 

 tend to perform oscillations in the same periodic time as in still water, by 

 the impulse and resistance of the particles of water against her keel and the 

 sharp parts of her hull, which tend, under certain circumstances, to make 

 her roll against the waves, that is, inclining towards the nearest wave-crest, 

 and by other circumstances. 



The tendency to keep upright to the effective wave-surface may be distin- 

 guished from the tendency to keep truly upright, by calling the former stiff- 

 ness and the latter steadiness. In smooth water stiffness and steadiness are 

 the same thing ; amongst waves they arc different, and to a certain extent 

 opposed ; that is to say, the means used for obtaining one of those qualities 

 are sometimes prejudicial to the other. Stiffness is favourable to the dry- 

 ness of the ship, and to the power of carrying sail ; steadiness is favourable 



