39 G EEPORT— 1891. 



tions of similarity have been fulfilled, while in no case has it fallen 

 decidedly below this value without decided symptoms of dissimilarity 

 having appeared, so that this value ibr the criterion seems to be esta- 

 blished as a good working rule for the formation of an estuary from 

 sand at the level of half-tide. 



If the bottom of the estuary is modelled the case is diflFerent, but the 

 occurrence of large ripples, in experiments in tank F and in Experiment V. 

 in tank E, when the value of the criterion fell as low as '08, shows that 

 the similarity of the ripple depends on the same value of the criterion as 

 the formation of the estuary. 



16. Experimenta ivith Limitivg Value of Criterion. — Experiment Y. 

 tuithLand Water, Tank E, Plates VIF., VIII., and XL, from November 20 to 

 December 24.^The conditions of this experiment were designed to bring 

 the value of the criterion, estimated from the rise of tide in the generator 

 in the final condition of equilibrium, to 0'09, keeping the horizontal scale 

 as nearly as possible the same as in IV., and diminishing the rise of tide so 

 as to increase the proportional depth of sand in the river, and thus pre- 

 vent the bottom being swept clean when the final condition was reached. 



The length of the crank working the generator in IV. had been 4'437 

 inches ; this was reduced to 377 inches in V.. reducing the rise of the 

 tide in the ratio 0'85. To keep the horizontal scale the same the period 

 33'3 seconds was increased to 36 seconds, leaving the product;; \//t constant. 



This reduced the vertical exaggeration e in the ratio 0"85. Thus the 

 value of h^e is reduced (0'85)^ or 0'5'2. 



Now the value of the criterion in Experiment IV. just before the 

 bottom was swept with sand was greater than 0'18, which, multiplied by 

 0-52, gives 0093. 



As carried out at the final condition shown in Plan 3, Plate VIII., the 

 period was 35'6 seconds, the rise of tide 0'107, and the value of the 

 criterion 00912. 



This low value of the criterion showed itself in the rate of progress of 

 the experiment. It was 13,000 tides before the sand in the river reached 

 Section 19, against 4,000 in Experiment IV., and 25,000 against 9,000 in 

 xV. before reaching the head of the river. In the early stage of the ex- 

 periment it seemed doubtful whether the sand was going to bar the river 

 as in Experiment IV., tank F. Except in rate of action, however, the 

 motion of the sand followed the same course as in Experiment IV., taking 

 a sudden shift at about 20,000 tides, and then rapidly lowering the sand 

 at the head of the estuary. At the mouth of the river the bottom of the 

 tank was reached after 50,000 tides, but only between the ripple bars, so 

 that it was not swept clean. 



The ripples in this experiment were very much larger than anything 

 before in tank E, showing that the criterion was approaching its critical 

 value. 



The final condition of the estuary, as shown in Plan 3, after 36,000 

 tides, shows conclusively the effect of the upper tidal water in a long 

 river on the bed of the lower estuary. Below Section 19, 32 miles from 

 the top of the river, there is no sand above the level of low water in the 

 estuary, and from this the sand falls uniformly to the mouth of the river, 

 where there is a depth of water, at low tide, of 30 feet. In the head of 

 the estuary there is a bar the top of which is only 12 feet below low 

 water ; this is at Section 9, or 18 miles below the mouth of the river ; 

 below this point the sand gradually falls to the generator. 



