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85.

superficies of ye water wch passeth thrô and morover it is supposed ye water equally swift at ye bottom and top and towards ye sides.

     Example

Let us suppose an Aqueduct wch is two foot large, and that ye water is a foot heigh and that in 20 seconds ye wax went 30 foot, that shall be 1 1/2 foot in a second, but because that ye water goeth slower at ye bottom than at ye top we must take but 20 foot, that shall be therefore 1 foot in a second, ye product of 1 foot heigh by 2 foot large is 2 wch multiplyed by 20 long gives 40 cubic foot or 40 times 35 pints of water wch maketh 1400, 60 seconds will give 3 times as much viz 4200 pints and dividing 4200 by 14 wch is ye number of pints an inch of water gives in a minute, or 60 seconds ye quotient will be 300, wch shall be ye number of inches wch ye Aqueduct will give.

  We may calculate easyly after this manner ye number of inches that ye river Seine will give:  For since their passeth below Pontronal in a minute 200000 cubic feet of water, if we multiply 35 wch is ye number of pints contained in a cubic foot, by 200000 we shall have 7000000 of pints being divided by 14 gives 500000 wch is ye number of inches ye River Seine gives when it is in its mean height:

  If we would calculate great holes as a Square Toise, we must consider ye height from ye surface of ye water above ye middle of ye Toise.  Let it be for example 5 feet, there will be therefore 8 feet to ye middle of ye Toise.  The product of 8 by 13 is 104 where at ye square root is 10 1/5 near, as 13 to 10 1/5 so is 14 to 11 near;  and [[strikethrough]] a round ye 3 lines [[/strikethrough]] because that an inch round is 16 times as great as a round of 3 lines an inch surmounted by 8 feet will give 16 times 11 pints, or 178 pints wch divided by 14 give 12 inches 4/7 for a hole of an inch diameter.  A hole of 12 4/7 by 144 is 1810;  ye foot round will give therefore 1810 inches.  Ye Toise round contains 36 times ye foot round, ye product of 36 by 1810 is 65160 as 11 to 14 so is 65160 to 82930:  Therefore ye Toise Square will give 82930 inches

  Whence is known that if ye river Seine had been retained when it is a little more than in its mean height, and that it was elevated to 8 feet above a square hole of 10 feet and of 18 feet large;  it would all pass thrô:  For it would have to the center of ye circle wch was 10 foot diameter, 13 feet from ye surface of ye retained water, and would give an inch into a hole of 3 lines diameter, thrô an inch diameter it would give 16 inches;  thrô a foot 144 times 16 inches wch make 2304 inches and multiplying that number by 100 ye square of 10 foot, wch is the largeness of ye hole, it would be 230400 and according ye proportion of ye circle to ye circumference Sq: wch is as 11 to 14, we shall find near 293236 square inches and adding to it 8 feet in length, we shall have more than 500000 inches, wch is what ye river Seine gives being moderate as hath been said above;  and by consequence it will pass all thrô a Sq hole wch is 18 foot large and 10 heigh.

  If ye water runs thrô an Aqueduct or thrô a chanell of a river according to an uniform small steepness, it will acquire in a moderate space a swiftness wch it will not augment:  For ye rubbing of ye sides and of the bottom of ye channel and ye [[?inserting]] of ye parts of ye water from above below and ye resistance of ye air to ye small waves wch are in its surface make it loose one part of its swiftness, and by consequence it can accelerate its motion but to a certain swiftness wch it will acquire in a little time:  Whence it follows that if a river hath run thrô a sufficiently long space in a certain declvity and that it runs afterwards thrô a declivity [[strikethrough]] and that it runs afterwards [[/strikethrough]] less steep, that is to say thrô a plain less inclined, it will diminish its swiftness:  For since it had acquired in ye first diclivity, all ye swiftness it could have there, wch it could not have acquired in a lesser, it follows that it will diminish its swiftness a little in that declivity wch is less, till it is reduced to ye swiftness it could acquire there

Transcription Notes:
mandc: Reviewed. 1 square Toise was about 3.799 square meters, about 40.9 sq ft. Desaguliers translates "square toise" as "square fathom."