92 Ocean Waves 



if the vessel be moving uniformly on her course : the periods 

 of the oscillations only will be affected : her angular position 

 with respect to the ridges remaining the same. 



Fig. 1] . Next, suppose the vessel be acted on by two systems 

 of waves, viz., a a, bb, c c, as before, and j? p, q q, r r, &c., pro- 

 gressing obliquely to them : and in the jDOsition denoted the 

 mast assume an angle with the vertical equal to 0. Now, if 

 the system a a progress with the same velocity as the system 

 p p (in which case they must be equal in magnitude { 8 [ ) ; 

 when the wave a has progressed to the position 6, p has 

 progressed to the position q, and the two systems are in the 

 same position as before with respect to the vessel : whence 

 the same inclination will be repeated with the passage of 

 each wave. 



If, however, the velocity of one system be n times that of 

 the other, n of the large (and therefore more rapid) waves 

 will have to pass before the next less one brings the two 

 systems into the same relative position with the body. In 

 this case therefore the vessel will repeat the same cycle of 

 movements ; hence, universally, if a floating body however 

 great float upon two or more systems of waves, and keep 

 the same course or angle with respect to them, her motions 

 upon them will be performed in regular cycles, each cycle 

 comprising as many passages of the largest system of waves 

 as is equal to the least common multiple of the velocities of 

 all the systems. 



27. The wave motions of a vessel of any size, steering a 

 uniform course at sea, therefore, instead of being irregular 

 follow these exact laws. In fact, we may imagine a resultant 

 wave and the position and oscillations of a floating body of 

 any magnitude or shape to be referable to those of an incon- 

 siderable body upon this resultant wave. The orbit of the 

 particles in such a wave would be elliptical, the elements of 

 the wave being peculiar to each vessel, according to her 

 magnitude and build. These elements can be accurately 

 obtained by observations on bodies entirely withinboard, as 

 will be subsequently shown. The period, dimensions, and 

 position of the hypothetical wave being thence deducible. 



Of course there are disturbing influences, such as imme- 

 diate effects of the wind, variations in the wave elements, 

 in the vessel's course, &c. Making allowaDces for these, 

 however, a long series of experiments would furnish reliable 

 if not very exact data for measurement of the mean elements 

 of resultant waves. 



