338 BEPOKT— 1889. 



Considering that 1 lb. in B is equivalent to 8 lbs. in A, and that 

 altogether in A there would be 1,100 lbs., B was left with about 7 per 

 cent, more sand in proportion than A. 



The experiment was then continued, the sand coming down in both 

 tanks, but not so as to get into the generators. The motion of the sand in 

 the two tanks followed almost exactly the same course, B gradually taking 

 the lead. In this case there was not the least sign of the middle channel in 

 B, the sand keeping level across and following the same course as had 

 previously been observed in Experiments 5 and 6 A. 



When B had run 16,570 tides it was stopped for surveying, while A 

 was allowed to run on to make up the number of tides. 



Surveys were then made. 



Discussion op the Results Obtained. 



Since the experiments have been arranged in accordance with the law 

 of kinetic similarity, followed in my previous experiments, it may be 

 well to restate this law before proceeding to discuss the results. 



If h be the depth of water in a uniform trough, it is well known that 

 the velocity of a wave, of which the length L compared with h is great, 

 and of which the height is proportional to li,, varies as the square root 

 of /;. 



For geometrical similarity at any instant the lengths of the troughs 

 must be proportional to L. 



The period of rise and fall, p, will thus be inversely proportional to 



L 

 Hence for the law of kinetic similarity, 



"~j|] (l) 



has a constant value for all scales. 



This law takes no account of the resistance of the bed, for a first 

 approximation to which the law would be 



iVA + A(l-B^) .... (2) 

 L 



constant, where A and B are constants to be determined by experiments. 



Since the comparative periods of the two tanks have been made 

 proportional to the square roots of their dimensions, e.g., the period of 

 tank A s/2 times the period of tank B, the bottom resistances produce 

 dynamically similar results. 



In comparing the results obtained with the same values of h in the 

 same tank with diiFerent periods, the bottom resistances would be 

 different, and this difference should appear in the results unless too small 

 to be appreciable, in which case the results would compare witb the 

 simple period. 



There are four other sources of possible divergence from the simple 

 dynamic law, which will become larger an the periods become slower and 

 the tide lower: — 



1. The drainage of the sand after the tide has left it supplies the low 

 water channels with a constant stream at low water ; the velocity of this 



