TRACT 38.

PROBLEMS.

373

Exam. 1 . For London-bridge.

By the observations made by Mr. Labelye in 1746,

The breadth of the Thames at London-bridge is 926 feet;The sum of the waterways at the time of low-water is 236 ft.;Mean velocity of the stream just above bridge is 3£ ft. per sec.But under almost all the arches are driven into the bed greatnumbers of what are called dripshot piles, to prevent the bedfrom being washed away by the fall. These dripshot pilesstill further contract the waterways, at least of their mea-sured breadth, or near 39 feet in the whole; so that thewaterway will be reduced to 197 feet, or in round numberssuppose 200 feet.

Then b = 926, c — 200, v = 3-J-

Hence

1-44 14—c*64c 2

1234765-40(00

64 x 40000

And v z — — 10^V

Theref. *467 x 10^=4-63 ft. = 4 ft. 8i in. the fall required.By the most exact observations made about the year 1736,the measure of the fall was 4 feet 9 inches.

Exam. 2. For Westminster-bridge.

Though the breadth of the river at Westminster-bridge is1220 feet; yet, at the time of the greatest fall, there is waterthrough only the 13 large arches, which amount to but 820feet; to which adding the breadth of the 12 intermediatepiers, equal to 174 feet, gives 994 for the breadth of theriver at that time; and the velocity of the water a little abovethe bridge, from many experiments, is not more 2j- feet persecond.

Here then b = 994, c = 820, v = 2\ —

Hence

1-44

64 c*

1422771-67240064 x 672400

= -017436.

And^=^=5 lV .

Theref. -017436 x 5-^—08827 ft. = l in. the fall required;