s 
departure, attains its own proper regimen. Bt 
ou will notice that this reasoning requires that there should 
be a rise and fall of the surface of the curve of amplitude I 
ve seen no such rise myself, nor been able to obtain 4 
existence appear to me too plain to be disputed. It must} 
necessity be extremely small,—too small perhaps for observati 
For the formula h = when applied to a 4 foot velocity gives 
us h = 0-25, and a velocity of 4:3 yields for h only h= 0263, 
By which we see that a rise which would only add a quantil 
= 0018 to the depth would increase the velocity full 7%. 
tendency to increase. Partly it assists, partly deadens. 
Again let us recur to our formula. Although made by W 
. g Ly 
_ We see that sin « is the measure of the slope of the original: 
. ‘. i 
— "ab 2g of the resistances of the whetted perimeter of 
pogl, whilst the denominator marks the changes whi 
the condition of the stream. ‘To use it for our 
vie must find the value of a, for some finite point on 
€ strea ee and then placing Palen Sn infinitesiin 
