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84.

               Explication in numbers

Let D B be 16 and B I 1, ye Sq Sq of I R shall be 1 if ye Sq Sq of D C is 16 and by consequence D C shall be 2 if I R is 1.  Let B I be a mean proportional between B I and B D, wch shall be by consequent 4:  Ye swiftness by ye weight I B shall be 4 if ye swiftness of ye weight D B is 16:  But ye circle or ye surface I R shall be one, and ye circle D C 4:  Therefore these quantitys will be as their swiftnesses and by consequence in ye same time ye circles or surfaces D C and I K will be run thrô:  And if there is need of 1 second of time for ye surface GK to run thrô its quadruple will run thrô in ye same time by a quadruple swiftness, ie ye surface D C since it is quadruple to ye other.  Ye same proportion will be found in all ye other surfaces, wch compose all ye water or in ye solids wch have a thickness infinitely small.  We suppose in all these experiments that there is no turning round in ye water nor any small hollow, as in vessels wch void themselves.

                 Rule.

If there be 2 pipes of equall height and unequal largness (whatforever their inequality is, and that ye water goeth out at their bottoms thrô equall holes there will no more water go out ye streight pipe than thrô ye larg in ye same time keeping them full provided that ye lesser pipe hath its diameter about 4 times as large as ye hole thrô wch ye water goeth out, and that ye water hath no circular motion in ye pipes:  For ye water going out thrô equall holes will elevate equal weights as is said above;  it will go therefore as swift in one as in ye other and by consequence there will go out as much water in ye same time:  

  If there is therefore a reservatory of 100 feet diameter, and one of a foot equall height, and peirced at ye bottom or at ye side with equal holes at ye same height from ye surface of ye water there will go out as much from one as from ye other in ye same time.

  If is made a question whether if there is 2 pipes of an inch large and inequal in height, for example one of 5 feet and ye other of 10 and that these were filled with water, if they would give as much water one as ye other because ye water in all ye two falls equally swift, as two unequall cylinders of ye same matter in ye beginning of their fall;  because ye air resists both very little and they are accelerated sensibly likewise according to odd numbers:  Therefore if there goeth out 6 feet of water in a certain time from one, there will go out as much from ye other.  But if we straiton ye great pipe to 4 lines at its base, it will give more water in ye first fourth of the second than if it were all open:  This is ye calculation.

  The product of 13 by 52 is 676 whereof ye root is 26, as 13 to 26:  14 pints to 28 therefore in a minute that hole will give 28 pints, or 56 pounds;  and by an hole of 4 lines 99 pounds 1/2 and in one 2d about 26 ounces and 1/2 and in 1/4 at a 2d 6 1/2 ounces:  But in one fourth of a 2d the cyclinder of water descends but 3/4 of a foot, wch upon ye largeness of an inch goeth a little more ye 4 ounces, therefore in 1/4 of a second there goeth out of ye great cylinder 2 1/2 ounces more water thrô ye hole of 4 lines, than from ye small cylinder all open:

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                  DISCOURS V            
      Of the measure of running waters
        in an Aqueduct or in a river

  To measure ye running waters in ye conduit of an Aqueduct or those of a river wch we canot receive into vessels we may observe the following method.

  We put upon ye water a boul of wax charged with a little heavier matter, so that there may very little of ye wax pass above ye water for fear of ye wind, and after having measured 20 or 15 feet long ye Aqueduct, we recounted with a pendulum of half seconds in what time ye boul of wax carried by cours of ye water will pass that distance afterwards we multiplied ye largeness of ye Aqueduct by ye height of ye water, and ye product by ye space ye wax run thrô ye last product wch is a solid did mark all ye water wch did pass in ye time observed thrô one part of ye Aqueduct to make that operation with justness, it is necessary that ye bed of ye water hath ye same steepness as the 

Transcription Notes:
mandc: Reviewed. Note that the section on this page titled "Discours V" is labeled "Discourse IV" in the Desaguliers translation. In that translation "boul of wax" is translated as "ball of wax.''