20 N. M. FENNEMAN 
be cited that perfect waves of the first order are produced experi- 
mentally by the sudden addition of water at one end Olea 
rectangular vessel, or by the immersion of a solid, or by a 
sudden pushing forward of the wall of the vessel, the effect in 
each case being the local raising of the water surface above the 
level of repose. A corresponding process in lakes or sea where 
the bottom becomes shallow may be found in the sudden deliv- 
ery of the mass of water which falls upon the front of a breaking 
wave. Observation on the shores of large water bodies, such as 
the great lakes, would indicate that the area over which waves 
show a translatory element is somewhat definitely limited by the 
breaker line. It is probable, however, that there is also a more 
gradual change by which the waves become increasingly positive 
as the water shallows and the features of waves of the first order 
are thereby assumed. 
If the modifications of oscillatory waves in shallowing water 
be reviewed while holding in mind the charactertistics of trans- 
latory waves as given above, it will be observed that these 
changes are all in the direction which would favor the conver- 
sion of oscillatory into translatory waves. This is seen in the 
increase of crests with corresponding disappearance of troughs ; 
the growing excess of the forward movement of particles over 
backward movement and the increased horizontal amplitude of 
the lower orbits, approaching equality with that of the orbits 
above. For present purposes it may suffice to adopt the con- 
ception of Mr. Russell’ who thought of the overgrown crest as 
«The wave of the second order may disappear and a wave of the first order take 
its place. The conditions under which I have observed this phenomenon are as fol- 
lows: one of the common sea waves, being of the second order, approaches the shore, 
consisting as usual of a negative or hollow part and of a positive part elevated above 
the level; and as formerly noted, 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 negative parts of the 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, falling into the hollow of the other, give rise to smooth 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 
