9. The great waves of translation are reflected from surfaces at right angles to the direction of their motion, without suffering -any change but that of direction.
10. The great primary waves of translation cross each other without change of any kind, in the same manner as the small oscillations pro duced on the surface of a pool by a falling stone.
11. The waves of the sea are not of the first order ; they belong to the second or oscillatory order of waves ' • they are partial displace ments at the surface which do not 'extend to considerable depths, and are therefore totally different in character from the great waves of translation, in which the motion of displacement of the particles of the fluid in the waves of the sea is greatest at the surface and diminishes rapidly. There are generally on the surface of the sea several co existent classes of oscillations of varying direction and magnitude, which by their union give the surface an appearance of irregularity which does not exist in nature.
12. 'When waves of the sea approach a shore or come into shallow water, they become waves of translation, and obeying the laws already mentioned, always break when the depth of the water is not greater than their height above the level.
13. Waves at the surface of the sea do not move with the velocity due to the whole depth of the fluid ; may they not move with the velocity due to that pert which they do agitate, or to some given part of it I 14. A circumstance frequently observed when the waves break on the shore, has been satisfactorily accounted for by the examination of the constitution of the-waves of the sea. It has been frequently ob served that a certain wave is the largest of a stories, and that these large waves occur periodically at equal intervals, so that sometimes every third wave, every seventh, or every ninth wave, is the largest. Now as there are almost always several coexistent series of waves, and as one of these is a long, gentle " under swell," propagated to the shore from — — the deep sea in the distance, while the others are short and more super ficial waves, generated by n temporary breeze of reflections from a neighbouring shore ; so it will follow that when the smaller waves are or Ith, or Łth, or in any other given ratio to the length of longer ones, thee° waves in which the ridges of the two series are coincident will be the periodical large waves ; and if there be three systems of coexistent waves, or any greater number, their coincidences will give periodical large recurring waves, having maxima and minima of various orders.
15. The tide-wave appears to be the only wave of the ocean which belongs to the first order, and appears to be identical with the great primary wave of translation ; its velocity diminishes and increases with the depth of the fluid, and appears to approximate closely to the velocity due to half the depth of the fluid in the rectangular channel. and to a certain mean depth which is that of the centre of gravity of the section of the channel. It is, however, difficult to determine the limits within which the tide-wave retains its unity ; where portions of the same channel differ much in depth at points remote from each other, the tide-waves appear to separate.
16. The tide appears to be a compound wave, one elementary woe bringing the first part of flood tide, another the high water, and so on ; these move with different velocities according to the depth. On ap proaching shallow shores the, anterior tide-waves move more slowly in the shallow water, while the posterior waves moving more rapidly, diminish the distance between successive waves. The tide-wave be comes thus dislocated, its anterior surface rising more rapidly and its posterior surface descending more slowly than in deep water.
17. A tidal bore [Bone] is formed when the water is so shallow at low water that the first waves of flood tide more with a velocity so much less than that due to the succeeding part of the tidal wave, as to be overtaken by the subsequent waves ; or wherever the tide rises so rapidly, and the water on the shore or in the river is so shallow, that the height of the first wave of the tide is greater than the depth of the fluid at that place. 'levee in deep water vessels are safe from the waves of rivers which injure those on the shore.