88 Ocean Waves 



the body round upon its centi-e of gravity g, until the lateral 

 pressures or immersions of the sides are equal ; that is until 

 ik\B parallel to a h. 



The body then assumes the position shown in (fig. 8, pZafe 1) 

 Let g shea, vertical line representing the weight of the body : 

 this is equivalent to two forces g r parallel with, and g t &t 

 right angles to the surface of the liquid a h : consequently, 

 t g a.t right angles to the surface will represent the force of 

 buoyancj^* Hence by parity of reasoning the force of 

 buoyancy acts everywhere at right angles to the surface of 

 wave, and therefore, 



19. A body floating on a wave will assume a position at 

 every point such that the plane of flotation will be parallel 

 to the wave surface at that point : the deviation of the mast 

 from the vertical being equal to the angle which the tangent 

 to the trochoidal surface at that point forms with the horizon. 

 Thus, (fig. 4, 2^late 2) different objects placed in the five points, 

 abed e will assume the angular positions shown. And one 

 object, suppose that at a, will, during the passage of a wave, 

 assume these positions successively. For from the defini- 

 tion (17)— 



20. A body floating on a wave travels in the same circular 

 orbit as the surface particles on which it rests. (Fig. 5, platel.) 

 Suppose the wave proceed from right to left, as shown by the 

 large arrow. During its passage the body at a performs 

 the circle abed, and at the same time has an angular 

 motion or oscillation about its centre of gravity, such that 

 the plane of flotation is everywhere a tangent to the surface ; 

 for instance, at b and d the plane is tangential to the curve 

 at e and/ on the same level. The velocity with which the 

 body is carried round is of course uniform, and in deep 

 water is always less than the horizontal velocity of the 

 wave. 



21. The absolute motion or locus described by a given 

 point of the floating body is an epicycloidal curve 

 resembling an elhpse, one of whose axes is the diame- 

 ter of the orbital circle. For instance, (fig. 6, plate 2) if a b 

 c d he the orbital circle as before, the mast-head will 



* Hence it appears that the common proposition that a floating body 

 displaces its own weight of water is incorrect, except in the case when the 

 the surface of the water in which it floats is horizontal. If 6 represent the 

 angle of inclination of the surface, and B the weight of the body, B cos 6 is 

 the true weight of the displaced water. Hence also, a body on the side of a 

 wave, is less immersed than when in the trough or on the summit. 



