426 SEVENTH REPORT—1837. 
are generally on the surface of the sea several coexistent 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 part which they do agitate, 
or to some given part of it ? 
14. A circumstance frequently observed when the waves break 
on the shore, has been satisfactorily accounted for by the ex- 
amination of the constitution of the waves of the sea. It has 
been frequently observed that a certain wave is the largest of a 
series, and that these large waves occur periodically at equal 
intervals, so that sometimes every 3rd wave, every 7th, or 
every 9th 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 a temporary breeze of reflections from 
a neighbouring shore ; so it will follow that when the smaller 
waves are 1, or 1, or 4th, or in any other given ratio to the 
length of longer ones, those 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 re- 
curring waves, having maxima and minima of various orders. 
15. The Tip—E Wave appears to be the only wave of the 
ocean which belongs to the first order, and appears to be iden- 
tical with the great primary wave of translation ; its velocity 
diminishes and increases with the depth of the fluid, and ap- 
pears 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 channei 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 
wave bringing the first part of flood tide, another the high 
water, and so on; these move with different velocities accord- 
ing to the depth. On approaching shallow shores the anterior 
