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78.

              DISCOURS III
    Of the measure of Spouts by the (ajutages) 
    [[space]] (fitting) of defferent holes

  We have see in ye 3d discource of ye 2d part that ye waters wch spout with equal swiftness thrô different holes make an equilibrium by their shoc wch weight wch are one to ye other in a subduple proportion of ye diameters of ye holes:  We may say ye same in respect of ye expence of water wch goeth thrô different passages at ye bottom of reservatorys of equal heights, viz that they expand their water in a subduple proportion of ye diameters of ye holes, it is demonstrated in this sort:

   Demonstration.

[[image: Top drawing of a plate C D with a tube M N piercing a hole in the plate at g h. Bottom drawing of a plate A B with a tube I L piercing a hole in the plate at e f.]]

A B is a plain perced with a round hole E F  C D is another plain pearced with another hole g h smaller than ye other, I L is a cylinder passing entirely thro ye in a certain time as of 2 seconds according to an uniform swiftness.  M N another cylinder of ye same length, but whose base is smaller, wch passeth also entirely thrô ye hole g h in ye same time of 2 seconds;  it is manifest that if ye diameter E f of ye cylinder I L wch is ye same with that of ye hole is double ye diameter g h ye great cylinder shall be 4 times ye other since they are one to ye other as their bases, whereof each is supposed equal to ye hole thrô wch it passeth:  Now since they go with ye same swiftness, when ye half of ye great cylinder shall be passed ye half of ye little one shall be passed also, and that wch shall be pressed of each shall be always in ye same proportion of 4 to 1:  Therefore if we suppose these cylinders to be spouts of water wch go with ye same swiftness, there will always pass in ye same time 4 times as much water thrô ye great hole as thrô the small which is ye double proportion of the diameters of ye holes, and ye same in respect of other proportions, to confirm this rule we made ye following experiments:

      Experiment I

  A reservatory having 12 feet 4 inches elevation, gave thrô a hole of 3 lines exactly measure 14 pints in 61 1/2 seconds, keeping it full, and thrô a [[strikethrough]] little [[/strikethrough]] hole of 6 lines exactly measured give ye same quantity of water in 15 1/2 seconds;  wch is near according to ye double proportion of ye diameters:  for there was given about 56 1/2 pints in ye time of 62 seconds

       Experiment II

  A reservatory of 24 feet 5 inches heigh gave thrô ye same hole of 3 lines 14 pints in 44 seconds 1/2 and another time in 45;  and ye hole of 6 lines gave them in 11 1/4 near and having repeated ye experiment it gave them in 11 seconds precisely.  By these 2 experiments and many other like wch were made in moderate heights from 5 to 27 feet, we found that different holes would give always water sensibly and near according to ye proportion of their surfaces and that we may follow this rule.

        Rule

    For the expence of spouts
  Spout of water of different holes placed below reservatorys equally heigh, give their water according to a double proportion of ye holes.

Transcription Notes:
mandc: Reviewed. Ajutages if French for spout. Translator never came back and filled in the blank. Subduple: in proportion of one to two. Added detailed image description. Changed capitalization on some letters, changed J to I. Image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&viewMode=images&mode=imagepath&pn=254&ww=0.09&wh=0.1898&wx=0.4705&wy=0.0351