372 REPORT — 1844. 



being cusped in form b\' the coincidence of tlie crests, they are in a position 

 of delicate equilibrium easily deranged ; and the derangement producing a 

 breaking of the wave, the disintegrated fragments of the smaller wave de- 

 tached from it, leave it smaller, and increase by an equal quantity the mag- 

 nitude of the larger. 



This exaggeration of an individual wave or group is increased by the 

 phsenomenon already noticed, that the velocity of wave trmismission may 

 be very different from the velocity of wave propagation. A large wave of 

 the sea remaining in a state of much slower motion than the motion of wave 

 transmission, being traversed by another series of different velocity, exposes 

 them successively on its summit to the increased action of the wind to disin- 

 tegration, thus making them tributary to its own further accumulation ; such 

 phenomena I have often noticed at sea ; the wave appears to over-run itself; 

 and the wave behind seems to take its place and acquire the magnitude and 

 form it has appeared to lose ; but it is the same wave which remains behind it, 

 and its motion is merely a deception, or rather it is as explained in a pre- 

 ceding paragraph. 



The final destruction of the waves of the sea, as they expend their strength 

 and conclude their existence on the rocks and sands of the shore, is a subject 

 of interesting study and observation. The sea-shore after a storm is a scene 

 of great grandeur ; it presents an instance of the expenditure of gigantic 

 forces, which impress the mind with the presence of elemental power as sub- 

 lime as the water-fall or the thunder. It is peculiarly instructive to watch 

 these waves as they near the shore : long before they reach the shore they 

 may be said to feel the bottom as the water becomes gradually more shallow, 

 for they become sensibly increased in height ; this increase goes on with the 

 diminution of depth and a diminution of length likewise as the wave becomes 

 sensible ; finally, the wave passes through the successive phases of cycloidal 

 form, as in Plate LVI., and becoming higher and more pointed, reaching the 

 limit of the cycloid, assumes a form of unstable equilibrium, totters, becomes 

 crested with foam, breaks with great violence, and continuing to break, is 

 gradually lessened in bulk until it ends in a fringed margin on the sea-shore. 



But there are a variety of questions to be determined concerning this shore 

 wave or breaking surf. Why and how does it break ? What happens after 

 it begins to break ? What are the relative levels of the waves and of the 

 water? What is the mean level of the sea, and what sort of waves are 

 breakers ? 



It is not at first obvious what form the mean level of the sea will assume 

 on a sloping beach sea-ward on which heavy breakers are rolling. It is 

 plainly not level ; the action of the wind is known to heap the water up on it. 

 The impetus of the waves also must raise it to some height due to their ve- 

 locity and force. Hence the mean surface of the sea will form a slope 

 upwards towards the sea-shore ; and this slope will form a continual and 

 imiform current of water outwards towards the sea, except when it is directly 

 opposed by the action of the wave in the opposite direction. 



There is a phaenomenon of some importance in breaking waves, to which 

 I have directed attention ; it is this, that the wave of the second order dis- 

 appears, and that a wave of the first order takes its place. It is to be observed 

 as follows : — In Avaves breaking on a shore, I have observed a phaenomenon 

 which is curious and not without importance. The wave of the second order 

 may disappear, and a wave of the first order take its place. The conditions 

 in which I have noticed this phaenomenon are as follows. One of the com- 

 mon sea M'aves, being of the second order, approaches the shore, consisting 

 as usual of a negative or hollow part, and of a positive part elevated above 



