and their Action on Floating Bodies. 93 



28. With regard to the action of wave forces on a floating 

 body, let us first take the case of a body of inconsiderable 

 magnitude. 



Thus, if the body be at the point B ; it is acted on by the 

 force of gravity, in. the direction Ba ; by the force of 

 buoyancy in the direction Bd ; perpendicular to the tangent 

 of the wave surface at B ; and by the moving force of the 

 particles in the direction Bf; tangential to the orbital circle 

 at B. Now, resolve the forces of gravity into the two forces 

 Be and Bh, tangential with and perpendicular to the 

 trochoidal surface. Then the constituent Bb and the force 

 of buoyancy Bd neutralise each other, and Be the resultant 

 of Be and Bf, will be the resultant force, the locus corres- 

 ponding to which is the orbital circle ; gravity being the 

 only one of the forces which is constant in direction. Hence, 

 therefore, the bodily motion of a floating body on a wave is 

 the resultant (variable) of three forces, viz. : the force of 

 gravity, the force of buoyancy, and the moving force of the 

 particles of water. 



No^v, the same proposition holds in the case of a body of 

 considerable magnitude, the only difference being, that the 

 force of buoyancy and the moving force of the particles are, 

 in this case, themselves resultant forces (25). 



The angular motion of the body round its centre of gravity 

 or wave axis, is due to the force of buoyancy alone, acting 

 in a variable direction by the shifting of the wave surface. 

 The force of buoyancy is consequently exerted in two ways, viz.: 

 in oscillating the body round its wave axis, and in moving 

 the axis bodily. Now, the force tending to move any 'point 

 within a vessel, is compounded of these : the part is moved 

 by the resultant of all the wave forces, and of the force of 

 gravity acting upon that part. 



29. The momentum of a floating body on a wave, is equal 

 to the momentum of the displaced water. For, as the body 

 displaces a weight of water equal to the force of buoyancy 

 (18), the result is the same as if the immersed part consisted 

 of particles of the liquid, or were part and parcel of the 

 wave. The wave force, therefore, exerted on floating bodies, 

 is proportional to the masses of such bodies. A large body 

 which subtends several waves, is of course acted upon by 

 mure forces than is a less body ; the rigidity of the body, in 

 fact, serves to oppose or unite the various forces. 



Thus, if the immersion of a body be ten times as great as 

 that of another body, and the direction of the level of the 



