ox WAVES. 373 



the level ; and as formerly noticed, this positive portion gradually increases 

 in height, and at length the wave breaks, and the positive part of the wave 

 falls forward into the negative part, filling up the hollow. Now we readily 

 enough conceive that if the positive and the negative part of a wave were 

 precisely equal in height, volume, and velocity, they would, by uniting, exactly 

 neutralize each other's motion, and the volume of the one filling the hollow 

 of the other,give rise tosmooth water; but in approaching the shore the positive 

 part increases in height, and the result of this is, to leave the positive portion 

 of the wave much in excess above the negative. After a wave has first been 

 made to break on the shore, it does not cease to travel, but if the slope be gentle, 

 the beach shallow and very extended (as it sometimes is for a mile inwards 

 from the breaking-point, if the waves be large), the whole inner portion of 

 the beach is covered with positive waves of the first order, from among which 

 all waves of the second order have disappeared. This accounts for the phae- 

 nomenon of breakers transporting shingle and wreck, and other substances 

 shorewards after a certain point ; at a great distance from shore, or whei-e 

 the shores are deep and abrupt, the wave is of the second order, and a body 

 floating near the surface is alternately carried forward and backward by the 

 waves, neither is the water affected to a great depth ; whereas nearer the 

 shore, the whole action of the wave is inwards, and the force extends to the 

 bottom of the water and stirs the shingle shorewards ; hence the abruptness 

 also of the shingle and sand near the margin of the shore where the breakers 

 generally run. 



I have observed this most strikingly exemplified in Dublin Bay after a 

 storm : there is a locality peculiarly favourable to the study of breaking 

 waves above Kingston, where over an extent of several miles there is a broad, 

 flat, sandy beach, varying in level very slightly and slowly. Waves coming 

 in from the deep sea are first broken when they approach the shallow beach 

 in the usual way ; they give off residuary waves, which are positive ; these 

 are %vide asunder from each other, are wholly positive, and the space between 

 them, several times greater than the amplitude of the wave, are perfectly flat, 

 and in this condition they extend over wide areas and travel to great dis- 

 tances. These residuary positive waves evidently prove the existence, and 

 represent the amount of the excess of the positive above the negative forces 

 in the wind wave of the second order. See Plate XLIX. fig. 7. 



