184 Dr. Young’s Hydraulic Investigations. 
e ~, /, % —f — •/(/- L — > ) : and in the same manner/is found, 
for the second case, equal to - -f- ~y[~‘ For example, 
suppose the height a 2 feet, b — c = 1 , and conse- 
quently e = 1, then d becomes i, z; = 4, and y = 8 ; and in 
the first case z — .1, and in the second 2 — .14. 
If u, the velocity of the obstacle, were great in comparison 
with m \/ ■ the velocity of a wave, and the space c below the 
obstacle were small, the anterior part of the elevation would 
advance with a velocity considerably greater than the natural 
velocity of the wave: but if the space below the obstacle 
bore a considerable proportion to the whole height, the ele- 
vation % would be very small, since a moderate pressure would 
cause the fluid to flow back, with a sufficient velocity, to ex- 
haust the greatest part of the accumulation, which would 
otherwise take place. Hence the elevation must always be 
less than that which is determined by the equation m \/ zc 
— ev, and z is at most equal to ~ b; but since 
the velocity of the anterior margin of the wave can never mate- 
rially exceed m\/ ~ , especially when z is small, and ~ 
being in this case nearly s/\ zy^a)7 & > m y/ ~ — m y/ b 
== m (y - 4~ y \za)d ' V b] which, multiplied by 2:, shows 
the utmost quantity of the fluid that can be supposed to be 
carried before the obstacle. Supposing b = j- a, this quan- 
tity becomes m \/ - . ~ ~ ; and if ^ be, for example, 
~ , it will be expressed by ^~ oq av, while the whole quan- 
tity of the fluid left behind. 
