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fallen to acquire the velocity (25b/21c)v. ---------- I. & II. Then (25b/21C)^2*vv/Aa - vv/Aa is the measure of the fall required. ----- VII. Or ((25b/21C)^2-1)*vv/Aa]] is a rule, by which the fall may by readily computed. Here [[underline]]a[[/underline]] = 16,0899 feet and A[[underline]]a[[/underline]] = 64,3596. EXAMPLE I. [[underline]]For London-bridge[[/underline]]. By the observations made by Mr. Labeleye 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 3 1/6 feet [[underline]]per[[/underline]] 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 1/6 of their measured breadth, or about 39 1/3 feet in the whole. So that the water-way will be reduced to 196 2/3 feet. Now b=926; c=196 2/3; v=3 1/6; Aa=64,3596. Then 25b/24c = 23150/4130 = 5,60532. And (5,60532)^2 = 31,4196; and 31,4196-1 = 30,4196 = (25b/21c)^2-1. Also vv = (19/6)^2 = 361/36; And vv/Aa = 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. EXAMPLE II. For Westminster-Bridge. Altho' the breadth of the river at Westminster Bridge is 1220 feet; yet, at the time of the greatest fall, there is water thro' [[strikethrough]]all the[[/strikethrough]] only the thirteen large arches, which amount to 820 set: to which adding the breadth of the twelve intermediate piers, equal to 174 feet, gives 994 for the breadth of the river at that time: and the velocity of the water just above the bridge (from many experiments) is not greater than 2 1/4 feet [[underline]]per[[/underline]] second. Here b=994; c=820; v=2 1/4; Aa=64,3596. Now 25b/21c = 24850/27220 = 1,443. And (1,443)^2 = 2,082; And 2,082-1 = 1,082 = (25b/21c)^2-1.