ON RIVERS AND ESTUARIES. 561 



to light by this model, which it is impossible for me here to notice without 

 unduly extending the length of this paper, if, indeed, I have not already 

 done so. I will therefore only remark that a second start was made 

 with the sand flat in this second model, and that the result obtained was 

 the same as regards the general features of the estuary. So interesting 

 were- these results that it was decided to try a larger scale. A model, 

 having a horizontal scale of H inches to a mile, and a vertical scale of 

 33 feet to an inch, was therefore made, and the tide produced as before. 

 The calculated period of this model is 80 seconds, and experiment bears 

 this out, any variation leading to some tidal phenomena, such as bonos 

 or standing waves, which are not observed ir the estuary. 



The disadvantage of the larger model is the time occupied — a little 

 more than a minute a tide — which means about 300 tides a day, or 2,000 

 tides a week. On one occasion the model was kept going for 6,000 tides, 

 and a survey was then made of the state of the sand. And this will be 

 seen to present a remarkable resemblance in the general features to the 

 charts of the Mersey, of which three — 1861, 1871, 1881 — are shown ; in 

 fact the survey from the model presents as great a resemblance to any 

 one of these as they do to each other. 



It is impossible for me to enter upon all the points of agreement. 

 Taking into account that in both the estuary and the model there are 

 always changes going on within certain limits, and these changes do 

 affect the currents to a certain extent, it is not to be supposed that there 

 will be exact agreement between the currents at all points and at all 

 states of the tides on the model and estuary. Still there is a general 

 agreement, and in the few verifications I have made I have found that 

 the cuiTent found in the model at a particular point and state of tide is 

 also to be found in the estuary. 



In one respect the great difference between the model and the estuary 

 calls for remark : this is the much greater depth of the model as com- 

 pared with its length and breadth. The vertical scale being 33 feet to 

 an inch, and the horizontal scale 880 feet to an inch, so that the vertical 

 heights are nearly twenty-seven times greater than the horizontal dis- 

 tances, such a difference is necessary to get any results at all with sach 

 small scale models ; and it is only natural to suppose that it would mate- 

 rially affect the action. As a matter of fact, however, it does not seem 

 to do so. And, further, it would seem that, notwithstanding the general 

 resemblance on the regime of the beds of large and small streams running 

 over sand, there is in these a similar difference in vertical scale, the 

 smaller streams not only having a greater slope, but also having greater 

 depth as compared with their breadth and steeper banks. So far as the 

 theory of hydi'odynamics will apply, it seems that in the model the 

 effects of the momentum of the water would be greater as compared 

 with the bottom resistances than in the estuary, and I think that they 

 are. But the effects of momentum in the estuary greatly preponderate 

 on the resistances, as shown by the fact that the tide at the top of the 

 flood rises some 2 to 3 feet higher at high spring tides than it does at the 

 rock ; nor does it do much more than this in the model. In the model it 

 certainly seems that the general regime is determined by the momentum 

 effects, and from the almost exact resemblance which this regime bears 

 to that of the estuary, it would seem that, although the momentum effects 

 may be diminished by the greater resistance on the bottom, they are still 

 the prevailing influence in determining the configuration of the banks. 



1887. 



