THE PRINCIPLES OF BRIDGES.

TRACT I.

Si

the breadth of the open chanel is to the breadth of the nar-row passages.

“ T. The quantity of the fall, caused by an obstacle in arunning stream, is measured by the difference between theheights fallen from, to acquire the velocities in the narrowpassages anJ open chanel.—For, just above the fall the velo-city of the stream is such, as would be acquired by a bodyfalling from a height higher than the surface of the water:and at the fall, the velocity of the stream is such, as wouldbe acquired by the fall of a heavy body from a height moreelevated than the top of the falling stream ; and consequentlythe real fall is less than this height. Now as the stream comesto the fall with a velocity belonging to a fall above its sur-face ; consequently the height belonging to the velocity atthe fall, must be diminished by the height belonging to thevelocity with which the stream arrives at the fall.

“ PROBLEM.

<£ In a chanel of running water, whose breadth is con-tracted by one or more obstacles; the breadth of the chanel,the mean velocity of the whole stream, and the breadth ofthe water-way between the obstacles, being given ; to findthe quantity of the fall occasioned by those obstacles.

“ Let b = breadth of the chanel in feet;

v = mean velocity of the water in feet per second;c = breadth of the water-way between the obstacles.

Now 25 : 21 :

• c • 2 1 r

And #c :b ::

2 of)v : —i21 c

vv .

Also ( 2 a) 1 : vo :

25b

And (2 af : (jf c v ) :

,25b w

'27c ' X 7a’ ^ ltto ^ or ^ ie velo-

2 5b

city — v, bv princ. 1 and 2.

J Cj, lc > „ I