STABILITY, PROPULSION, AND SEA-GOING QUALITIES OF SHIPS. 33 



'No wave can be sharper thau a cycloidal wave ; for if the trochoid were 

 looped, the particles in the loop would be unsupported. When the wave 

 form tends to pass the cycloid, it must break. 



The extreme obsei'ved height of ocean-waves appears to be about 40 feet, 

 and the greatest observed length 600 feet ; these would have a periodic time 

 of 11 seconds (roughly); their crest would advance at a rate of 33 knots an 

 hour, and the velocity of the siirf ace -particles would be about 11"4 feet per 

 second. In short waves of the same height the particles of water move 

 faster, in the inverse ratio of the period ; but the mass of moving water at 

 the crest of the longer wave is the greater in the ratio of 



where X and X' are tlie lengths, and h the height. If, therefore, the above- 

 mentioned wave were shortened to 200 feet, the surface-particles would be 

 moving at a note of 20 feet a second, while the mass of water in the crest 

 would be about one-sixth. From such data it is easy to infer both the de- 

 structive eft'ect of impact from the top of a wave, and the relative quantity 

 of water which a ship would take on board in shipping a sea. 



The front and rear of a trochoidal wave are exactly similar. Observation, 

 as well as theory, shows that this is true to an extent not commonly believed 

 for ordinary waves. The exceptions are, when the wind is sufficient to push 

 the tops of the waves at extra speed, and when the water shoals rapidly. 

 But oven here the relative steepness of the advancing face is exaggerated by 

 most observers. Until a wave is about to break, the actual difference of slope 

 remains very small. 



It should be borne in mind that circular orbits and trochoidal wave- 

 surfaces are only approximations, although near enough to the truth for 

 Ijurposes connected with the rolling of ships. In particular, it appears both 

 from theory and obsei'vatiou that there is almost always some progressive 

 motion combined with the orbital motion ; and also that waves begin to break 

 long before their crests attain a form so sharp as that of the cusped cycloid, 

 the two slopes at the crest of a breaking wave cutting each other at right 

 angles, or nearly so*. 



The ordinary wave of a rough sea is usually an aggregate of waves of 

 different period, and not unfrequently of different direction. For rough 

 purposes, it is sufficient to draw each system of waves separately and add 

 their corresponding ordinates, to get the resulting surface. This can hardly 

 be reUed i;pon in extreme cases ; and, in any case, the motion of each par- 

 ticle is not according to any one or more wave-systems separately, but it is a 

 motion compounded of what would bo due to each separately if the otlacrs 

 were not. 



Oscillations of a Shijp among Waves, 



A Treatise on ' Shipbuilding : Theoretical and Practical f,' edited by Pro- 

 fessor Rankine, contains, in a very clear and condensed form, a n'siime of 

 nearly all that was known on this subject up to 1SG4 inclusive. The fol- 

 lowing abstract is chiefly taken from that work :-~ 



It is to be observed that what follows relates to the compositioir of the 

 ship's oscillation with that of a simple trochoidal Wave. The complete pro- 

 blem of a ship's behaviour, depending as it does on wind, waves, roUing, 

 pitching, dipping, yaAving, variable head-resistance and lateral resistance, 



* See Phil. Mag. Not. 1861. t See pp. 72, 77 of that work. 



1869. D 



