By the observations made by Mr. Labelye in 1746,
The breadth of the Thames at London-bridge is 926 feet;
The sum of the water-ways at the time of the greatest fall is 236 feet;
The mean velocity of the stream taken at its surface just above bridge
is 3⅙ feet _per_ second.
Under almost all the arches there are great numbers of drip-shot piles,
or piles driven into the bed of the water-way, to prevent it from being
washed away by the fall. These drip-shot piles considerably contract
the water-ways, at least ⅙ of their measured breadth, or about 39⅓ feet
in the whole.
So that the water-way will be reduced to 196⅔ feet.
Now _b_ = 926; _c_ = 196⅔; _v_ = 3⅙; 4_a_ = 64,3596.
Then 25_b_ ⁄ 21_c_ = 23150 ⁄ 4130 = 5,60532.
And 5,60532² = 31,4196; and 31,4196 - 1 = 30,4196 = (25_b_ ⁄ 21_c_)² -
1.
Also _vv_ = (19 ⁄ 6)² = 361 ⁄ 36; And _vv_ ⁄ 4_a_ = 361 ⁄ (36 ×
64,3596) = 0,15581.
Then 30,4196 × 0,15581 = 4,739 feet, the fall sought after.
By the most exact observations made about the year 1736, the measure of
the fall was 4 feet 9 inches.