' ON THE ACTION OF WAVES AND CURRENTS. 517 
8. The Value of the Criterion for V-shaped Estuaries.—This critical 
value of C deduced from the experiments in rectangular tanks appears 
to correspond very well with the results of the experiments in the V-shaped 
estuaries. In the experiments Table I. with V-shaped estuaries in the 
small tank, the value of C is in no case far from the critical value ‘09 or 
either side. In Experiment IX., B, however, the value of C at starting was 
only 0-046 as in 1., B, and in consequence of the observed sluggishness 
and local character of the action in the lower estuary, the rise of tide 
was increased from 0-088 to 0°11, which remedied the action and raised 
the criterion to 0°101, and in Experiments X. and XII., B, and in I,, D, 
the values are between 0°095 and 0:°084. In Experiments II., D, F, and 
¥’, owing to the falling off in the tide in consequence of the addition of 
the river, the criterion is as low as 0°073. In these experiments signs of 
sluggishness and local action in the lower estuary were observed at 
starting, and the difference in the action of the upper estuary as compared 
with Tank E in respect of closing up the tidal river may have been due 
to tke low value of the criterion. 
In the experiments in the large tanks the values of C are all well 
above the critical value: the nearest are the experiments in Tank KE, 
©=0°'17, which is only double the critical value, and the action was as 
quick and general as in the case where C=0°5. 
It may be noticed that the range through which the value of C asa 
criterion has been tested is small. Had the form of criterion been appre- 
hended sooner this might have been somewhat extended, though con- 
siderable adaptation of the apparatus would be required to carry it far. 
, 9. If C=0-08 
With a tide 0-1 ft. the greatest period is 32 secs. and least exaggeration 80. 
af 0°12 ft. a AS 60 secs. fi 5 47. 
<3 0-14 ft. “c re 102 secs. 3 = 30. 
= O72 it. fr rf 6 mins. 9 secs. 5 A 10. 
. 0:43 ft. - °; 1h. 33 m. 48 s. Fs PP 1. 
From which the size of tanks and length of periods necessary to verify 
this law for exaggerations of less than thirty can be seen. 
10. The General Distribution of Sand in V-shaped Estuaries.—The 
experiments all show that with sufficiently high values of the criterion, 
as in the rectangular tanks so in those of symmetrical V-shape, the sand 
arrives at a definite general state of equilibrium after a definite number 
of tides. This state in the rectangular tanks was a general slope which 
corresponded to a definite curve, twelve miles long as reduced by the 
kinetic law to a 30-foot tide, between the contours at high and low water in 
the generator. This slope was furrowed by 3 or 4 shallow channels at 
distances of some two miles, commencing very gradually at the top and 
dying out at some distance below low water. In the V-shaped estuaries 
the state of equilibrium differs from that in the rectangular tanks in a 
very systematic manner ; it consists in a main low-water channel com- 
mencing at the end and extending all the way down the V out into the 
parallel portion of the tank. If this channel is in the middle it is the 
only channel, but if, as is as often as not the case, it takes one side of the 
estuary, then at the lower end there is on the other side a second channel 
starting at some distance down the estuary. The height of the banks 
above the bottom of the main low-water channel towards the lower end 
of the V is much greater than in the rectangular estuaries. No general 
methed of comparing the general slope or distribution of the sand in the 
