and their Action on Floating Bodies. 91 



resultant of these forces. Hence the angle of inclination 

 which she assumes will determine her position upon the 

 resultant wave. 



Fig. 9. Forinstance, supposed, beasmallbody upon thelower 

 part of a wave, a h progressing from right to left. A being 

 inconsiderable the force of buoyancy is in tlie single direction 

 shown by the arrow d (18), and being in the lower part of 

 the wave, the body partakes singly of the moving force of 

 the wave in the retrogade direction, shown by the arrow e 

 (22). Now, suppose a very large body B B of similar figure 

 to A, and whose centre of gravity is in the same point, be 

 held in a similar position to A as shown in the figure. The 

 body B covers the whole wave surface c ah, and is acted on 

 by the force of buoyancy in all the various directions shown 

 by the small arrows at light angles to the surface ; the 

 resultant of which is such that B cannot maintain the same 

 position as A ; for resolving the force of buoyancy into the 

 hydrostatic pressure on the sides h f, f g and g c, and taking 

 g h equal to b f, the force of buoyancy, that is the pressure 

 of the water to fill up the displacement, acts on the sides f g 

 and h c (since b f and h g neutralise each other) will force 

 the body round by virtue of the preponderating force on h c. 

 Again, since B covers the summit as well as the trough, the 

 moving force of the wave urges it on at the summit and 

 backward in the trough (23). On account of these con- 

 flicting actions, the body B moves only partially with the 

 particles of water in which it floats, and therefore as the 

 positions of the waves constantly shift with respect to it, the 

 motion of a large body floating on waves may be described 

 as a ceaseless attempt to obtain an equilibrium which it 

 never acquires.* 



26. Fig. 10. But, whatever be the composite motion of the 

 body B, this motion will be regular, that is it will be regularly 

 repeated on the same system of waves. For, suppose the 

 body B rest upon a series of parallel waves a a, b b, c c, 

 progressing in the direction shown by the arrow, and in the 

 position shown, the mast will assume an angle with the ver- 

 tical equal to 0. Then the waves being uniform when b has 

 progressed to c, « has progressed to b ; the relative position 

 on the waves being similar ; consequently, as like causes 

 produce like effects, the mast will assume the same angle 

 with the vertical as before. Nor will the result be aflected 



* See the footuote, § 46. 



