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tween the heights fallen from to acquire the veloci- 
ties in the narrow paftages and open chanel. 
For juft above the fall, the velocity of the ftream 
is fuch, as would be acquired by a body falling 
from a height higher than the furface of the 
water : 
And at the fall, the velocity of the ftream is 
fuch, as would be acquired by the fall of a body 
from a height more elevated than the top of the 
falling ftream ; and confequently the real fall is 
lefs than this height. 
Now as the ftream comes to the fall with a 
velocity belonging to a fall above its furface ; 
Confequently the height belonging to the velo- 
city at the fall muft be diminifhed by the height 
belonging to the velocity, with which the ftream 
arrives at the fall. 
Problem. 
In a chanel of running water , whofe breadth is con- 
trail ed by one or more objlacles the breadth of 
the chanel , the mean velocity of the whole ftream , 
and the breadth of the water-way between the ob- 
ftacles being given ; To find the quantity of the 
fall occafioned by thofe objlacles . 
Let b = breadth of the chanel in feet. 
v = mean velocity of the water in feet per fee. 
c = breadth of the water-way between the 
obftacles. 
Now 2$ z 21 :: c z ~ c the water-way con- 
traded . . . Principle III. 
And 
