ON WAVES. 427 
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 becomes thus dis- 
located, its anterior surface rising more rapidly, and its pos- 
terior surface descending more slowly than in deep water. 
17. A tidal bore is formed when the water is so shallow at 
low water that the first waves of flood tide move 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. Hence in 
deep water vessels are safe from the waves of rivers which in- 
jure those on the shore. 
18. The identity of the tide wave, and of the great wave of 
translation, show the nature of certain variations in the esta- 
blishment of ports situated on tidal rivers. Any change in the 
depth of the rivers produces a corresponding change on the 
interval between the moon’s transit and the high water imme- 
diately succeeding. It appears from the observations in this 
report, that the mean time of high water has been rendered 37 
minutes earlier than formerly by deepening a portion of about 
12 miles in the channel of a tidal river, so that a tide wave 
which formerly travelled at the rate of 10 miles an hour, now 
travels at the rate of nearly 15 miles an hour. 
19. It also appears that a large wave or a wave of high 
water of spring tides travels faster than a wave of high water 
of neap tides, showing that there is a variation on the establish- 
ment, or on the interval between the moon’s transit and the 
succeeding high water, due to the depth of the fluid at high 
water, and which should, of course, enter as an element into 
the calculation of tide tables for an inland port derived from 
those of a port on the sea shore. The variation of the interval 
will vary with the square root of mean depth of the channel 
at high water. 
These results give us principles, 1st, for the construction of 
canals ; 2nd, for the navigation of canals ; 3rd, for the improve- 
ment of tidal rivers ; 4th, for the navigation of tidal rivers ; 5th, 
for the improvement of tide tables.—See the Transactions of 
the Sections at the end of the volume. 
